|
#SIXFORMAT GapDocGAP
HELPBOOKINFOSIXTMP := rec(
encoding := "UTF-8",
bookname := "groupoids",
entries :=
[ [ "Title page", "0.0", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5"
],
[ "Abstract", "0.0-1", [ 0, 0, 1 ], 26, 2, "abstract", "X7AA6C5737B711C89" ]
,
[ "Copyright", "0.0-2", [ 0, 0, 2 ], 59, 2, "copyright",
"X81488B807F2A1CF1" ],
[ "Acknowledgements", "0.0-3", [ 0, 0, 3 ], 69, 2, "acknowledgements",
"X82A988D47DFAFCFA" ],
[ "Table of Contents", "0.0-4", [ 0, 0, 4 ], 78, 3, "table of contents",
"X8537FEB07AF2BEC8" ],
[ "\033[1X\033[33X\033[0;-2YIntroduction\033[133X\033[101X", "1",
[ 1, 0, 0 ], 1, 5, "introduction", "X7DFB63A97E67C0A1" ],
[ "\033[1X\033[33X\033[0;-2YMany-object structures\033[133X\033[101X", "2",
[ 2, 0, 0 ], 1, 6, "many-object structures", "X8361CEA4856430C6" ],
[ "\033[1X\033[33X\033[0;-2YMagmas with objects; arrows\033[133X\033[101X",
"2.1", [ 2, 1, 0 ], 19, 6, "magmas with objects arrows",
"X7920BF45828AE5DE" ],
[ "\033[1X\033[33X\033[0;-2YSemigroups with objects\033[133X\033[101X",
"2.2", [ 2, 2, 0 ], 168, 9, "semigroups with objects",
"X7FDF94E8791B9BC1" ],
[ "\033[1X\033[33X\033[0;-2YMonoids with objects\033[133X\033[101X", "2.3",
[ 2, 3, 0 ], 230, 10, "monoids with objects", "X86C32E6981557ED0" ],
[
"\033[1X\033[33X\033[0;-2YGenerators of magmas with objects\033[133X\033[10\
1X", "2.4", [ 2, 4, 0 ], 269, 11, "generators of magmas with objects",
"X842D1B0C7A76CC15" ],
[
"\033[1X\033[33X\033[0;-2YStructures with more than one piece\033[133X\033[\
101X", "2.5", [ 2, 5, 0 ], 314, 11, "structures with more than one piece",
"X7C7007207FD91BB0" ],
[
"\033[1X\033[33X\033[0;-2YMappings of many-object structures\033[133X\033[1\
01X", "3", [ 3, 0, 0 ], 1, 13, "mappings of many-object structures",
"X78FC7902804CED8E" ],
[
"\033[1X\033[33X\033[0;-2YHomomorphisms of magmas with objects\033[133X\\
033[101X", "3.1", [ 3, 1, 0 ], 24, 13, "homomorphisms of magmas with objects",
"X82F856A086B93832" ],
[
"\033[1X\033[33X\033[0;-2YHomomorphisms of semigroups and monoids with obje\
cts\033[133X\033[101X", "3.2", [ 3, 2, 0 ], 103, 15,
"homomorphisms of semigroups and monoids with objects",
"X7C4D1AEE80D41A35" ],
[
"\033[1X\033[33X\033[0;-2YHomomorphisms to more than one piece\033[133X\\
033[101X", "3.3", [ 3, 3, 0 ], 157, 16, "homomorphisms to more than one piece"
, "X795C8DE37AED7B44" ],
[
"\033[1X\033[33X\033[0;-2YMappings defined by a function\033[133X\033[101X"
, "3.4", [ 3, 4, 0 ], 210, 17, "mappings defined by a function",
"X7B9D71BB7BAEFAAA" ],
[ "\033[1X\033[33X\033[0;-2YGroupoids\033[133X\033[101X", "4", [ 4, 0, 0 ],
1, 18, "groupoids", "X82F6A1AB798648F4" ],
[
"\033[1X\033[33X\033[0;-2YGroupoids: their properties and attributes\033[13\
3X\033[101X", "4.1", [ 4, 1, 0 ], 41, 18,
"groupoids: their properties and attributes", "X7AC321DC7E3C6167" ],
[
"\033[1X\033[33X\033[0;-2YGroupoid elements; stars; costars; homsets\033[13\
3X\033[101X", "4.2", [ 4, 2, 0 ], 333, 24,
"groupoid elements stars costars homsets", "X7F23BE3F85C9BA06" ],
[ "\033[1X\033[33X\033[0;-2YSubgroupoids\033[133X\033[101X", "4.3",
[ 4, 3, 0 ], 461, 26, "subgroupoids", "X7BDBA72C852C4625" ],
[ "\033[1X\033[33X\033[0;-2YLeft, right and double cosets\033[133X\033[101X"
, "4.4", [ 4, 4, 0 ], 722, 30, "left right and double cosets",
"X831AA9E8780235F2" ],
[ "\033[1X\033[33X\033[0;-2YConjugation\033[133X\033[101X", "4.5",
[ 4, 5, 0 ], 828, 32, "conjugation", "X8653FC9786E3209A" ],
[
"\033[1X\033[33X\033[0;-2YGroupoids formed using isomorphisms\033[133X\033[\
101X", "4.6", [ 4, 6, 0 ], 922, 34, "groupoids formed using isomorphisms",
"X86DD749283068705" ],
[
"\033[1X\033[33X\033[0;-2YGroupoids whose objects form a monoid\033[133X\\
033[101X", "4.7", [ 4, 7, 0 ], 1005, 35,
"groupoids whose objects form a monoid", "X795DEB3D825B2120" ],
[ "\033[1X\033[33X\033[0;-2YHomomorphisms of Groupoids\033[133X\033[101X",
"5", [ 5, 0, 0 ], 1, 38, "homomorphisms of groupoids",
"X879ED2A7878B5A7A" ],
[
"\033[1X\033[33X\033[0;-2YHomomorphisms from a connected groupoid\033[133X\\
033[101X", "5.1", [ 5, 1, 0 ], 41, 38,
"homomorphisms from a connected groupoid", "X85D28690823636CD" ],
[
"\033[1X\033[33X\033[0;-2YProperties and attributes of groupoid homomorphis\
ms\033[133X\033[101X", "5.2", [ 5, 2, 0 ], 118, 40,
"properties and attributes of groupoid homomorphisms",
"X7BFF46FD8308846F" ],
[
"\033[1X\033[33X\033[0;-2YProperties of a groupoid homomorphism\033[133X\\
033[101X", "5.2-1", [ 5, 2, 1 ], 121, 40,
"properties of a groupoid homomorphism", "X83DDA9528396451A" ],
[
"\033[1X\033[33X\033[0;-2YAttributes of a groupoid homomorphism\033[133X\\
033[101X", "5.2-2", [ 5, 2, 2 ], 151, 40,
"attributes of a groupoid homomorphism", "X870565948381B921" ],
[
"\033[1X\033[33X\033[0;-2YSpecial types of groupoid homomorphism\033[133X\\
033[101X", "5.3", [ 5, 3, 0 ], 252, 42,
"special types of groupoid homomorphism", "X7DBC80D8817CDA04" ],
[
"\033[1X\033[33X\033[0;-2YHomomorphisms to a connected groupoid\033[133X\\
033[101X", "5.4", [ 5, 4, 0 ], 440, 45,
"homomorphisms to a connected groupoid", "X7EAAB2A97E097FB6" ],
[
"\033[1X\033[33X\033[0;-2YHomomorphisms to more than one piece\033[133X\\
033[101X", "5.5", [ 5, 5, 0 ], 511, 47, "homomorphisms to more than one piece"
, "X795C8DE37AED7B44" ],
[ "\033[1X\033[33X\033[0;-2YAutomorphisms of Groupoids\033[133X\033[101X",
"6", [ 6, 0, 0 ], 1, 49, "automorphisms of groupoids",
"X803E01577A2B37D2" ],
[
"\033[1X\033[33X\033[0;-2YAutomorphisms of single piece groupoids\033[133X\\
033[101X", "6.1", [ 6, 1, 0 ], 8, 49,
"automorphisms of single piece groupoids", "X7935832881320667" ],
[
"\033[1X\033[33X\033[0;-2YAutomorphisms of a groupoid with rays\033[133X\\
033[101X", "6.1-3", [ 6, 1, 3 ], 196, 52,
"automorphisms of a groupoid with rays", "X8278B93E7F78038C" ],
[ "\033[1X\033[33X\033[0;-2YInner automorphisms\033[133X\033[101X",
"6.1-5", [ 6, 1, 5 ], 323, 54, "inner automorphisms",
"X7EC237ED7E1978B0" ],
[
"\033[1X\033[33X\033[0;-2YMatrix representations of groupoids\033[133X\033[\
101X", "6.2", [ 6, 2, 0 ], 491, 57, "matrix representations of groupoids",
"X8003AF117B956D16" ],
[ "\033[1X\033[33X\033[0;-2YGroupoid actions\033[133X\033[101X", "6.3",
[ 6, 3, 0 ], 553, 58, "groupoid actions", "X7DB8E7EF7A51F1BE" ],
[
"\033[1X\033[33X\033[0;-2YGraphs of Groups and Groupoids\033[133X\033[101X"
, "7", [ 7, 0, 0 ], 1, 61, "graphs of groups and groupoids",
"X78063DC8847554B4" ],
[ "\033[1X\033[33X\033[0;-2YDigraphs\033[133X\033[101X", "7.1",
[ 7, 1, 0 ], 13, 61, "digraphs", "X7D554C5D7FDC3D02" ],
[ "\033[1X\033[33X\033[0;-2YGraphs of Groups\033[133X\033[101X", "7.2",
[ 7, 2, 0 ], 65, 62, "graphs of groups", "X7BAFCA3680E478AE" ],
[
"\033[1X\033[33X\033[0;-2YWords in a Graph of Groups and their normal forms\
\033[133X\033[101X", "7.3", [ 7, 3, 0 ], 187, 64,
"words in a graph of groups and their normal forms",
"X7BD9DCF87FB3E0AF" ],
[
"\033[1X\033[33X\033[0;-2YFree products with amalgamation and HNN extension\
s\033[133X\033[101X", "7.4", [ 7, 4, 0 ], 273, 65,
"free products with amalgamation and hnn extensions",
"X7D99A7B37B36BAA8" ],
[
"\033[1X\033[33X\033[0;-2YGraphsOfGroupoids and their Words\033[133X\033[10\
1X", "7.5", [ 7, 5, 0 ], 444, 68, "graphsofgroupoids and their words",
"X78108FB4814AE887" ],
[ "\033[1X\033[33X\033[0;-2YDouble Groupoids\033[133X\033[101X", "8",
[ 8, 0, 0 ], 1, 72, "double groupoids", "X83B7E8A287C9284A" ],
[ "\033[1X\033[33X\033[0;-2YSingle piece double groupoids\033[133X\033[101X"
, "8.1", [ 8, 1, 0 ], 23, 72, "single piece double groupoids",
"X780DA94780938851" ],
[
"\033[1X\033[33X\033[0;-2YHorizontal and vertical groupoids in \033[22X\\
342\226\241(G)\033[122X\033[101X\027\033[1X\027\033[133X\033[101X", "8.1-8",
[ 8, 1, 8 ], 466, 80, "horizontal and vertical groupoids in a\226\241 g"
, "X7B8DEF5A7B5AEC46" ],
[
"\033[1X\033[33X\033[0;-2YDouble groupoids with more than one piece\033[133\
X\033[101X", "8.2", [ 8, 2, 0 ], 489, 81,
"double groupoids with more than one piece", "X7F319AA17ED13024" ],
[
"\033[1X\033[33X\033[0;-2YGenerators of a double groupoid\033[133X\033[101X\
", "8.3", [ 8, 3, 0 ], 535, 82, "generators of a double groupoid",
"X78E24657817C4D30" ],
[
"\033[1X\033[33X\033[0;-2YWhat is the double groupoid generated by a set of\
squares?\033[133X\033[101X", "8.3-3", [ 8, 3, 3 ], 591, 83,
"what is the double groupoid generated by a set of squares?",
"X85A6C1A685357E66" ],
[ "\033[1X\033[33X\033[0;-2YStarting with two groupoids\033[133X\033[101X",
"8.4", [ 8, 4, 0 ], 616, 83, "starting with two groupoids",
"X80E0318F78D2AD28" ],
[ "\033[1X\033[33X\033[0;-2YDouble groupoid homomorphisms\033[133X\033[101X"
, "8.5", [ 8, 5, 0 ], 666, 84, "double groupoid homomorphisms",
"X83F6AFC185148621" ],
[ "\033[1X\033[33X\033[0;-2YTechnical Notes\033[133X\033[101X", "9",
[ 9, 0, 0 ], 1, 86, "technical notes", "X7F2BA6DC7AD84FBC" ],
[ "\033[1X\033[33X\033[0;-2YMany object structures\033[133X\033[101X",
"9.1", [ 9, 1, 0 ], 9, 86, "many object structures",
"X7C5B725A7AED3C8D" ],
[ "\033[1X\033[33X\033[0;-2YMany object homomorphisms\033[133X\033[101X",
"9.2", [ 9, 2, 0 ], 104, 88, "many object homomorphisms",
"X7A4760E887C9C968" ],
[ "\033[1X\033[33X\033[0;-2YDevelopment History\033[133X\033[101X", "10",
[ 10, 0, 0 ], 1, 89, "development history", "X810C43BC7F63C4B4" ],
[ "\033[1X\033[33X\033[0;-2YVersions of the Package\033[133X\033[101X",
"10.1", [ 10, 1, 0 ], 4, 89, "versions of the package",
"X8192EA4C7B7CC5CD" ],
[ "\033[1X\033[33X\033[0;-2YWhat needs to be done next?\033[133X\033[101X",
"10.2", [ 10, 2, 0 ], 67, 90, "what needs to be done next?",
"X82148FB77CC3CCC0" ],
[ "Bibliography", "bib", [ "Bib", 0, 0 ], 1, 91, "bibliography",
"X7A6F98FD85F02BFE" ],
[ "References", "bib", [ "Bib", 0, 0 ], 1, 91, "references",
"X7A6F98FD85F02BFE" ],
[ "Index", "ind", [ "Ind", 0, 0 ], 1, 92, "index", "X83A0356F839C696F" ],
[ "\033[2XMagmaWithObjects\033[102X", "2.1-1", [ 2, 1, 1 ], 40, 6,
"magmawithobjects", "X7C51D7847BD23284" ],
[ "\033[2XSinglePieceMagmaWithObjects\033[102X", "2.1-1", [ 2, 1, 1 ], 40,
6, "singlepiecemagmawithobjects", "X7C51D7847BD23284" ],
[ "\033[2XObjectList\033[102X for magmas with objects", "2.1-1",
[ 2, 1, 1 ], 40, 6, "objectlist for magmas with objects",
"X7C51D7847BD23284" ],
[ "\033[2XRootObject\033[102X for magmas with objects", "2.1-1",
[ 2, 1, 1 ], 40, 6, "rootobject for magmas with objects",
"X7C51D7847BD23284" ],
[ "\033[2XIsDomainWithObjects\033[102X", "2.1-2", [ 2, 1, 2 ], 87, 7,
"isdomainwithobjects", "X87D1C0BC86749E6D" ],
[ "\033[2XIsMagmaWithObjects\033[102X", "2.1-2", [ 2, 1, 2 ], 87, 7,
"ismagmawithobjects", "X87D1C0BC86749E6D" ],
[ "\033[2XArrow\033[102X", "2.1-3", [ 2, 1, 3 ], 104, 7, "arrow",
"X86247DFC8242CEBE" ],
[ "\033[2XElementOfArrow\033[102X for magmas with objects", "2.1-3",
[ 2, 1, 3 ], 104, 7, "elementofarrow for magmas with objects",
"X86247DFC8242CEBE" ],
[ "\033[2XTailOfArrow\033[102X for magmas with objects", "2.1-3",
[ 2, 1, 3 ], 104, 7, "tailofarrow for magmas with objects",
"X86247DFC8242CEBE" ],
[ "\033[2XHeadOfArrow\033[102X for magmas with objects", "2.1-3",
[ 2, 1, 3 ], 104, 7, "headofarrow for magmas with objects",
"X86247DFC8242CEBE" ],
[ "\033[10XIsMultiplicativeElementWithObjects\033[110X", "2.1-3",
[ 2, 1, 3 ], 104, 7, "ismultiplicativeelementwithobjects",
"X86247DFC8242CEBE" ],
[ "\033[2XIsSinglePieceDomain\033[102X", "2.1-4", [ 2, 1, 4 ], 139, 8,
"issinglepiecedomain", "X7B3352148103FD05" ],
[ "\033[2XIsSinglePiece\033[102X", "2.1-4", [ 2, 1, 4 ], 139, 8,
"issinglepiece", "X7B3352148103FD05" ],
[ "\033[2XIsDirectProductWithCompleteDigraph\033[102X", "2.1-4",
[ 2, 1, 4 ], 139, 8, "isdirectproductwithcompletedigraph",
"X7B3352148103FD05" ],
[ "\033[2XIsDiscreteMagmaWithObjects\033[102X", "2.1-4", [ 2, 1, 4 ], 139,
8, "isdiscretemagmawithobjects", "X7B3352148103FD05" ],
[ "\033[2XSemigroupWithObjects\033[102X", "2.2-1", [ 2, 2, 1 ], 171, 9,
"semigroupwithobjects", "X8519787D833653A7" ],
[ "\033[2XSinglePieceSemigroupWithObjects\033[102X", "2.2-1", [ 2, 2, 1 ],
171, 9, "singlepiecesemigroupwithobjects", "X8519787D833653A7" ],
[ "\033[2XMagmaWithSingleObject\033[102X for semigroups", "2.2-1",
[ 2, 2, 1 ], 171, 9, "magmawithsingleobject for semigroups",
"X8519787D833653A7" ],
[ "\033[2XIsSemigroupWithObjects\033[102X", "2.2-1", [ 2, 2, 1 ], 171, 9,
"issemigroupwithobjects", "X8519787D833653A7" ],
[ "\033[2XMonoidWithObjects\033[102X", "2.3-1", [ 2, 3, 1 ], 233, 10,
"monoidwithobjects", "X7A271B1A7F2FF245" ],
[ "\033[2XSinglePieceMonoidWithObjects\033[102X", "2.3-1", [ 2, 3, 1 ],
233, 10, "singlepiecemonoidwithobjects", "X7A271B1A7F2FF245" ],
[ "\033[2XIsMonoidWithObjects\033[102X", "2.3-1", [ 2, 3, 1 ], 233, 10,
"ismonoidwithobjects", "X7A271B1A7F2FF245" ],
[ "\033[2XGeneratorsOfMagmaWithObjects\033[102X", "2.4-1", [ 2, 4, 1 ],
272, 11, "generatorsofmagmawithobjects", "X83239B307EE95054" ],
[ "\033[2XGeneratorsOfSemigroupWithObjects\033[102X", "2.4-1", [ 2, 4, 1 ],
272, 11, "generatorsofsemigroupwithobjects", "X83239B307EE95054" ],
[ "\033[2XGeneratorsOfMonoidWithObjects\033[102X", "2.4-1", [ 2, 4, 1 ],
272, 11, "generatorsofmonoidwithobjects", "X83239B307EE95054" ],
[ "\033[2XUnionOfPieces\033[102X for magmas with objects", "2.5-1",
[ 2, 5, 1 ], 317, 11, "unionofpieces for magmas with objects",
"X781FB06382E08115" ],
[ "\033[2XPieces\033[102X for magmas with objects", "2.5-1", [ 2, 5, 1 ],
317, 11, "pieces for magmas with objects", "X781FB06382E08115" ],
[ "\033[2XPieceOfObject\033[102X", "2.5-1", [ 2, 5, 1 ], 317, 11,
"pieceofobject", "X781FB06382E08115" ],
[ "\033[2XMagmaWithObjectsHomomorphism\033[102X", "3.1-1", [ 3, 1, 1 ], 27,
13, "magmawithobjectshomomorphism", "X86E00FEA7FF38FEA" ],
[ "\033[2XHomomorphismFromSinglePiece\033[102X", "3.1-1", [ 3, 1, 1 ], 27,
13, "homomorphismfromsinglepiece", "X86E00FEA7FF38FEA" ],
[ "\033[2XHomomorphismToSinglePiece\033[102X for magmas with objects",
"3.1-1", [ 3, 1, 1 ], 27, 13,
"homomorphismtosinglepiece for magmas with objects",
"X86E00FEA7FF38FEA" ],
[ "\033[2XMappingToSinglePieceData\033[102X for magmas with objects",
"3.1-1", [ 3, 1, 1 ], 27, 13,
"mappingtosinglepiecedata for magmas with objects", "X86E00FEA7FF38FEA"
], [ "\033[2XPiecesOfMapping\033[102X", "3.1-1", [ 3, 1, 1 ], 27, 13,
"piecesofmapping", "X86E00FEA7FF38FEA" ],
[ "\033[2XIsomorphismNewObjects\033[102X for magmas with objects", "3.1-1",
[ 3, 1, 1 ], 27, 13, "isomorphismnewobjects for magmas with objects",
"X86E00FEA7FF38FEA" ],
[ "\033[10XIsMappingToSinglePieceRep\033[110X", "3.1-1", [ 3, 1, 1 ], 27,
13, "ismappingtosinglepiecerep", "X86E00FEA7FF38FEA" ],
[ "\033[10XSource\033[110X", "3.1-1", [ 3, 1, 1 ], 27, 13, "source",
"X86E00FEA7FF38FEA" ],
[ "\033[10XRange\033[110X", "3.1-1", [ 3, 1, 1 ], 27, 13, "range",
"X86E00FEA7FF38FEA" ],
[ "\033[2XHomomorphismByUnion\033[102X for magmas with objects", "3.3-1",
[ 3, 3, 1 ], 160, 16, "homomorphismbyunion for magmas with objects",
"X7AE44D9485EB50F1" ],
[ "\033[2XIsInjectiveOnObjects\033[102X", "3.3-2", [ 3, 3, 2 ], 185, 16,
"isinjectiveonobjects", "X7C053B0379DDCE13" ],
[ "\033[2XIsSurjectiveOnObjects\033[102X", "3.3-2", [ 3, 3, 2 ], 185, 16,
"issurjectiveonobjects", "X7C053B0379DDCE13" ],
[ "\033[2XIsBijectiveOnObjects\033[102X", "3.3-2", [ 3, 3, 2 ], 185, 16,
"isbijectiveonobjects", "X7C053B0379DDCE13" ],
[ "\033[2XIsEndomorphismWithObjects\033[102X", "3.3-2", [ 3, 3, 2 ], 185,
16, "isendomorphismwithobjects", "X7C053B0379DDCE13" ],
[ "\033[2XIsAutomorphismWithObjects\033[102X", "3.3-2", [ 3, 3, 2 ], 185,
16, "isautomorphismwithobjects", "X7C053B0379DDCE13" ],
[ "\033[2XMappingWithObjectsByFunction\033[102X", "3.4-1", [ 3, 4, 1 ],
213, 17, "mappingwithobjectsbyfunction", "X81B64F9A855D265F" ],
[ "\033[2XIsMappingWithObjectsByFunction\033[102X", "3.4-1", [ 3, 4, 1 ],
213, 17, "ismappingwithobjectsbyfunction", "X81B64F9A855D265F" ],
[ "\033[2XUnderlyingFunction\033[102X", "3.4-1", [ 3, 4, 1 ], 213, 17,
"underlyingfunction", "X81B64F9A855D265F" ],
[ "", "4.0", [ 4, 0, 0 ], 1, 18, "", "X82F6A1AB798648F4" ],
[ "\033[2XSinglePieceGroupoid\033[102X", "4.1-1", [ 4, 1, 1 ], 44, 18,
"singlepiecegroupoid", "X8406913B7ED86CFE" ],
[ "\033[2XGroupoid\033[102X", "4.1-1", [ 4, 1, 1 ], 44, 18, "groupoid",
"X8406913B7ED86CFE" ],
[ "\033[2XMagmaWithSingleObject\033[102X for groups", "4.1-1", [ 4, 1, 1 ],
44, 18, "magmawithsingleobject for groups", "X8406913B7ED86CFE" ],
[ "\033[2XIsGroupoid\033[102X", "4.1-1", [ 4, 1, 1 ], 44, 18, "isgroupoid",
"X8406913B7ED86CFE" ],
[ "standard groupoid", "4.1-1", [ 4, 1, 1 ], 44, 18, "standard groupoid",
"X8406913B7ED86CFE" ],
[ "\033[2XObjectList\033[102X for groupoids", "4.1-2", [ 4, 1, 2 ], 99, 19,
"objectlist for groupoids", "X813B084184AAA890" ],
[ "\033[2XRootObject\033[102X for groupoids", "4.1-2", [ 4, 1, 2 ], 99, 19,
"rootobject for groupoids", "X813B084184AAA890" ],
[ "\033[2XRootGroup\033[102X", "4.1-2", [ 4, 1, 2 ], 99, 19, "rootgroup",
"X813B084184AAA890" ],
[ "\033[2XObjectGroup\033[102X", "4.1-2", [ 4, 1, 2 ], 99, 19,
"objectgroup", "X813B084184AAA890" ],
[ "\033[2XIsPermGroupoid\033[102X", "4.1-3", [ 4, 1, 3 ], 131, 20,
"ispermgroupoid", "X8511D3EE845CC930" ],
[ "\033[2XIsPcGroupoid\033[102X", "4.1-3", [ 4, 1, 3 ], 131, 20,
"ispcgroupoid", "X8511D3EE845CC930" ],
[ "\033[2XIsFpGroupoid\033[102X", "4.1-3", [ 4, 1, 3 ], 131, 20,
"isfpgroupoid", "X8511D3EE845CC930" ],
[ "\033[2XIsMatrixGroupoid\033[102X", "4.1-3", [ 4, 1, 3 ], 131, 20,
"ismatrixgroupoid", "X8511D3EE845CC930" ],
[ "\033[2XIsFreeGroupoid\033[102X", "4.1-3", [ 4, 1, 3 ], 131, 20,
"isfreegroupoid", "X8511D3EE845CC930" ],
[ "\033[2XUnionOfPieces\033[102X for groupoids", "4.1-4", [ 4, 1, 4 ], 166,
21, "unionofpieces for groupoids", "X8681D15C7CA15F87" ],
[ "\033[2XPieces\033[102X for groupoids", "4.1-4", [ 4, 1, 4 ], 166, 21,
"pieces for groupoids", "X8681D15C7CA15F87" ],
[ "\033[2XSize\033[102X", "4.1-4", [ 4, 1, 4 ], 166, 21, "size",
"X8681D15C7CA15F87" ],
[ "\033[2XReplaceOnePieceInUnion\033[102X", "4.1-4", [ 4, 1, 4 ], 166, 21,
"replaceonepieceinunion", "X8681D15C7CA15F87" ],
[ "\033[10XObjectList\033[110X for groupoids", "4.1-4", [ 4, 1, 4 ], 166,
21, "objectlist for groupoids", "X8681D15C7CA15F87" ],
[ "\033[2XHomogeneousGroupoid\033[102X", "4.1-5", [ 4, 1, 5 ], 222, 22,
"homogeneousgroupoid", "X855F318181808814" ],
[ "\033[2XPieceIsomorphisms\033[102X", "4.1-5", [ 4, 1, 5 ], 222, 22,
"pieceisomorphisms", "X855F318181808814" ],
[ "\033[2XHomogeneousDiscreteGroupoid\033[102X", "4.1-5", [ 4, 1, 5 ], 222,
22, "homogeneousdiscretegroupoid", "X855F318181808814" ],
[ "\033[10XIsHomogeneousDomainWithObjects\033[110X", "4.1-5", [ 4, 1, 5 ],
222, 22, "ishomogeneousdomainwithobjects", "X855F318181808814" ],
[ "\033[10XIsHomogeneousDiscreteGroupoidRep\033[110X", "4.1-5",
[ 4, 1, 5 ], 222, 22, "ishomogeneousdiscretegroupoidrep",
"X855F318181808814" ],
[ "\033[2XDirectProductOp\033[102X", "4.1-6", [ 4, 1, 6 ], 292, 23,
"directproductop", "X78E8FE0C7F599F5A" ],
[ "\033[2XProjection\033[102X for groupoids", "4.1-6", [ 4, 1, 6 ], 292,
23, "projection for groupoids", "X78E8FE0C7F599F5A" ],
[ "\033[2XEmbedding\033[102X for groupoids", "4.1-6", [ 4, 1, 6 ], 292, 23,
"embedding for groupoids", "X78E8FE0C7F599F5A" ],
[ "\033[2XGroupoidElement\033[102X", "4.2-1", [ 4, 2, 1 ], 336, 24,
"groupoidelement", "X7D028B3B8385ED07" ],
[ "\033[2XElementOfArrow\033[102X for groupoids", "4.2-1", [ 4, 2, 1 ],
336, 24, "elementofarrow for groupoids", "X7D028B3B8385ED07" ],
[ "\033[2XTailOfArrow\033[102X for groupoids", "4.2-1", [ 4, 2, 1 ], 336,
24, "tailofarrow for groupoids", "X7D028B3B8385ED07" ],
[ "\033[2XHeadOfArrow\033[102X for groupoids", "4.2-1", [ 4, 2, 1 ], 336,
24, "headofarrow for groupoids", "X7D028B3B8385ED07" ],
[ "\033[2XIsGroupoidElement\033[102X", "4.2-1", [ 4, 2, 1 ], 336, 24,
"isgroupoidelement", "X7D028B3B8385ED07" ],
[ "\033[10XArrow\033[110X for groupoid elements", "4.2-1", [ 4, 2, 1 ],
336, 24, "arrow for groupoid elements", "X7D028B3B8385ED07" ],
[ "* for groupoid elements", "4.2-1", [ 4, 2, 1 ], 336, 24,
"* for groupoid elements", "X7D028B3B8385ED07" ],
[ "\033[2XIdentityArrow\033[102X", "4.2-2", [ 4, 2, 2 ], 374, 24,
"identityarrow", "X78C3228682279032" ],
[ "inverse arrow", "4.2-2", [ 4, 2, 2 ], 374, 24, "inverse arrow",
"X78C3228682279032" ],
[ "\033[2XOrder\033[102X", "4.2-3", [ 4, 2, 3 ], 391, 25, "order",
"X84F59A2687C62763" ],
[ "loop", "4.2-3", [ 4, 2, 3 ], 391, 25, "loop", "X84F59A2687C62763" ],
[ "\033[2XObjectStar\033[102X", "4.2-4", [ 4, 2, 4 ], 407, 25,
"objectstar", "X7B561BAE7D471C60" ],
[ "\033[2XObjectCostar\033[102X", "4.2-4", [ 4, 2, 4 ], 407, 25,
"objectcostar", "X7B561BAE7D471C60" ],
[ "\033[2XHomset\033[102X", "4.2-4", [ 4, 2, 4 ], 407, 25, "homset",
"X7B561BAE7D471C60" ],
[ "", "4.2-4", [ 4, 2, 4 ], 407, 25, "", "X7B561BAE7D471C60" ],
[ "", "4.2-4", [ 4, 2, 4 ], 407, 25, "", "X7B561BAE7D471C60" ],
[ "\033[2XSubgroupoid\033[102X", "4.3-1", [ 4, 3, 1 ], 464, 26,
"subgroupoid", "X80780D287EDDB7BB" ],
[ "\033[2XIsSubgroupoid\033[102X", "4.3-1", [ 4, 3, 1 ], 464, 26,
"issubgroupoid", "X80780D287EDDB7BB" ],
[ "\033[2XIsWideSubgroupoid\033[102X", "4.3-1", [ 4, 3, 1 ], 464, 26,
"iswidesubgroupoid", "X80780D287EDDB7BB" ],
[ "\033[2XIsFullSubgroupoid\033[102X", "4.3-1", [ 4, 3, 1 ], 464, 26,
"isfullsubgroupoid", "X80780D287EDDB7BB" ],
[ "\033[2XSubgroupoidByObjects\033[102X", "4.3-2", [ 4, 3, 2 ], 483, 26,
"subgroupoidbyobjects", "X8600FA7B8051C9AC" ],
[ "\033[2XSubgroupoidBySubgroup\033[102X", "4.3-2", [ 4, 3, 2 ], 483, 26,
"subgroupoidbysubgroup", "X8600FA7B8051C9AC" ],
[ "\033[2XSubgroupoidWithRays\033[102X", "4.3-3", [ 4, 3, 3 ], 513, 27,
"subgroupoidwithrays", "X873E0914871858E8" ],
[ "\033[2XRaysOfGroupoid\033[102X", "4.3-3", [ 4, 3, 3 ], 513, 27,
"raysofgroupoid", "X873E0914871858E8" ],
[ "\033[2XRayArrowsOfGroupoid\033[102X", "4.3-3", [ 4, 3, 3 ], 513, 27,
"rayarrowsofgroupoid", "X873E0914871858E8" ],
[ "\033[2XSubgroupoidByPieces\033[102X", "4.3-4", [ 4, 3, 4 ], 563, 28,
"subgroupoidbypieces", "X7AEA9BF780CD6957" ],
[ "\033[2XPiecePositions\033[102X", "4.3-5", [ 4, 3, 5 ], 614, 29,
"piecepositions", "X78C7A83980BAE937" ],
[ "\033[2XFullTrivialSubgroupoid\033[102X", "4.3-6", [ 4, 3, 6 ], 646, 29,
"fulltrivialsubgroupoid", "X7FE8F09A7C8CEC5B" ],
[ "\033[2XDiscreteTrivialSubgroupoid\033[102X", "4.3-6", [ 4, 3, 6 ], 646,
29, "discretetrivialsubgroupoid", "X7FE8F09A7C8CEC5B" ],
[ "trivial subgroupoid", "4.3-6", [ 4, 3, 6 ], 646, 29,
"trivial subgroupoid", "X7FE8F09A7C8CEC5B" ],
[ "tree groupoid", "4.3-6", [ 4, 3, 6 ], 646, 29, "tree groupoid",
"X7FE8F09A7C8CEC5B" ],
[ "identity subgroupoid", "4.3-6", [ 4, 3, 6 ], 646, 29,
"identity subgroupoid", "X7FE8F09A7C8CEC5B" ],
[ "\033[2XDiscreteSubgroupoid\033[102X", "4.3-7", [ 4, 3, 7 ], 667, 29,
"discretesubgroupoid", "X7ACFBE7D855A82A3" ],
[ "\033[2XHomogeneousDiscreteSubgroupoid\033[102X", "4.3-7", [ 4, 3, 7 ],
667, 29, "homogeneousdiscretesubgroupoid", "X7ACFBE7D855A82A3" ],
[ "\033[2XMaximalDiscreteSubgroupoid\033[102X", "4.3-7", [ 4, 3, 7 ], 667,
29, "maximaldiscretesubgroupoid", "X7ACFBE7D855A82A3" ],
[ "\033[2XSinglePieceSubgroupoidByGenerators\033[102X", "4.3-8",
[ 4, 3, 8 ], 699, 30, "singlepiecesubgroupoidbygenerators",
"X7A9F29BD7D64DCC1" ],
[ "", "4.4", [ 4, 4, 0 ], 722, 30, "", "X831AA9E8780235F2" ],
[ "", "4.4", [ 4, 4, 0 ], 722, 30, "", "X831AA9E8780235F2" ],
[ "\033[2XRightCoset\033[102X", "4.4-1", [ 4, 4, 1 ], 725, 30,
"rightcoset", "X8412ABD57986B9FC" ],
[ "\033[2XRightCosetRepresentatives\033[102X", "4.4-1", [ 4, 4, 1 ], 725,
30, "rightcosetrepresentatives", "X8412ABD57986B9FC" ],
[ "\033[2XRightCosets\033[102X", "4.4-1", [ 4, 4, 1 ], 725, 30,
"rightcosets", "X8412ABD57986B9FC" ],
[ "\033[2XLeftCoset\033[102X", "4.4-1", [ 4, 4, 1 ], 725, 30, "leftcoset",
"X8412ABD57986B9FC" ],
[ "\033[2XLeftCosetRepresentatives\033[102X", "4.4-1", [ 4, 4, 1 ], 725,
30, "leftcosetrepresentatives", "X8412ABD57986B9FC" ],
[ "\033[2XLeftCosetRepresentativesFromObject\033[102X", "4.4-1",
[ 4, 4, 1 ], 725, 30, "leftcosetrepresentativesfromobject",
"X8412ABD57986B9FC" ],
[ "\033[2XLeftCosets\033[102X", "4.4-1", [ 4, 4, 1 ], 725, 30,
"leftcosets", "X8412ABD57986B9FC" ],
[ "\033[2XDoubleCoset\033[102X", "4.4-1", [ 4, 4, 1 ], 725, 30,
"doublecoset", "X8412ABD57986B9FC" ],
[ "\033[2XDoubleCosetRepresentatives\033[102X", "4.4-1", [ 4, 4, 1 ], 725,
30, "doublecosetrepresentatives", "X8412ABD57986B9FC" ],
[ "\033[2XDoubleCosets\033[102X", "4.4-1", [ 4, 4, 1 ], 725, 30,
"doublecosets", "X8412ABD57986B9FC" ],
[ "\\^ for arrows", "4.5", [ 4, 5, 0 ], 828, 32, "^ for arrows",
"X8653FC9786E3209A" ],
[ "\033[2X\\^\033[102X", "4.5-1", [ 4, 5, 1 ], 831, 32, "^",
"X7D21FB1A7D21FB1A" ],
[ "\\^ for groupoids", "4.5-1", [ 4, 5, 1 ], 831, 32, "^ for groupoids",
"X7D21FB1A7D21FB1A" ],
[ "\033[2XConjugateGroupoid\033[102X", "4.5-2", [ 4, 5, 2 ], 904, 34,
"conjugategroupoid", "X78218F357BFEDE82" ],
[ "\033[2XGroupoidByIsomorphisms\033[102X", "4.6-1", [ 4, 6, 1 ], 937, 34,
"groupoidbyisomorphisms", "X7B066DE28574A768" ],
[ "\033[2XIsGroupoidByIsomorphisms\033[102X", "4.6-1", [ 4, 6, 1 ], 937,
34, "isgroupoidbyisomorphisms", "X7B066DE28574A768" ],
[ "\033[2XSinglePieceGroupoidWithRays\033[102X", "4.7-1", [ 4, 7, 1 ],
1015, 36, "singlepiecegroupoidwithrays", "X805FA9F687C7F2A7" ],
[ "\033[2XRightActionGroupoid\033[102X", "4.7-2", [ 4, 7, 2 ], 1047, 36,
"rightactiongroupoid", "X7E399664868937C8" ],
[ "\033[2XIsGroupoidWithMonoidObjects\033[102X", "4.7-2", [ 4, 7, 2 ],
1047, 36, "isgroupoidwithmonoidobjects", "X7E399664868937C8" ],
[ "\033[2XGroupoidHomomorphismFromSinglePiece\033[102X", "5.1-1",
[ 5, 1, 1 ], 44, 38, "groupoidhomomorphismfromsinglepiece",
"X870288C6803D9005" ],
[ "\033[2XGroupoidHomomorphism\033[102X", "5.1-1", [ 5, 1, 1 ], 44, 38,
"groupoidhomomorphism", "X870288C6803D9005" ],
[ "\033[2XIsGroupoidHomomorphism\033[102X", "5.1-1", [ 5, 1, 1 ], 44, 38,
"isgroupoidhomomorphism", "X870288C6803D9005" ],
[ " for groupoid homomorphisms", "5.2-1", [ 5, 2, 1 ], 121, 40,
"for groupoid homomorphisms", "X83DDA9528396451A" ],
[ " for groupoid homomorphisms", "5.2-1", [ 5, 2, 1 ], 121, 40,
"for groupoid homomorphisms", "X83DDA9528396451A" ],
[ " for groupoid homomorphisms", "5.2-1", [ 5, 2, 1 ], 121, 40,
"for groupoid homomorphisms", "X83DDA9528396451A" ],
[ " for groupoid homomorphisms", "5.2-1", [ 5, 2, 1 ], 121, 40,
"for groupoid homomorphisms", "X83DDA9528396451A" ],
[ " for groupoid homomorphisms", "5.2-1", [ 5, 2, 1 ], 121, 40,
"for groupoid homomorphisms", "X83DDA9528396451A" ],
[ " for groupoid homomorphisms", "5.2-1", [ 5, 2, 1 ], 121, 40,
"for groupoid homomorphisms", "X83DDA9528396451A" ],
[ " for groupoid homomorphisms", "5.2-1", [ 5, 2, 1 ], 121, 40,
"for groupoid homomorphisms", "X83DDA9528396451A" ],
[ "\033[2XRootGroupHomomorphism\033[102X", "5.2-3", [ 5, 2, 3 ], 183, 41,
"rootgrouphomomorphism", "X85A99D8A83511DDE" ],
[ "\033[2XImagesOfObjects\033[102X", "5.2-4", [ 5, 2, 4 ], 191, 41,
"imagesofobjects", "X837EEB9578EA1A78" ],
[ "\033[2XImageElementsOfRays\033[102X", "5.2-5", [ 5, 2, 5 ], 198, 41,
"imageelementsofrays", "X791DC3F3852A6422" ],
[ "\033[2XMappingToSinglePieceData\033[102X for groupoids", "5.2-6",
[ 5, 2, 6 ], 216, 41, "mappingtosinglepiecedata for groupoids",
"X8391526C7A02FF19" ],
[ "\033[2XObjectGroupHomomorphism\033[102X", "5.2-7", [ 5, 2, 7 ], 237, 42,
"objectgrouphomomorphism", "X7C6775A178DB9D39" ],
[ "\033[2XInclusionMappingGroupoids\033[102X", "5.3-1", [ 5, 3, 1 ], 260,
42, "inclusionmappinggroupoids", "X855DB6C8815CDCC3" ],
[ "\033[2XRestrictedMappingGroupoids\033[102X", "5.3-2", [ 5, 3, 2 ], 280,
43, "restrictedmappinggroupoids", "X7946BC207D455A98" ],
[ "\033[2XParentMappingGroupoids\033[102X", "5.3-2", [ 5, 3, 2 ], 280, 43,
"parentmappinggroupoids", "X7946BC207D455A98" ],
[ "\033[2XIsomorphismNewObjects\033[102X for groupoids", "5.3-3",
[ 5, 3, 3 ], 304, 43, "isomorphismnewobjects for groupoids",
"X83B8AB6D7C9DB264" ],
[ "\033[2XIsomorphismStandardGroupoid\033[102X", "5.3-4", [ 5, 3, 4 ], 339,
44, "isomorphismstandardgroupoid", "X87C54BB581181400" ],
[ "\033[2XIsomorphismPermGroupoid\033[102X", "5.3-5", [ 5, 3, 5 ], 394, 45,
"isomorphismpermgroupoid", "X7CF33CCD8278A904" ],
[ "\033[2XRegularActionHomomorphismGroupoid\033[102X", "5.3-5",
[ 5, 3, 5 ], 394, 45, "regularactionhomomorphismgroupoid",
"X7CF33CCD8278A904" ],
[ "\033[2XIsomorphismPcGroupoid\033[102X", "5.3-5", [ 5, 3, 5 ], 394, 45,
"isomorphismpcgroupoid", "X7CF33CCD8278A904" ],
[ "\033[2XHomomorphismToSinglePiece\033[102X for groupoids", "5.4-1",
[ 5, 4, 1 ], 443, 45, "homomorphismtosinglepiece for groupoids",
"X8700B5977B2513C1" ],
[ "\033[2XGroupoidHomomorphismFromHomogeneousDiscrete\033[102X", "5.4-2",
[ 5, 4, 2 ], 480, 46, "groupoidhomomorphismfromhomogeneousdiscrete",
"X87225D86785DEBC2" ],
[ "\033[2XHomomorphismByUnion\033[102X for groupoids", "5.5-1",
[ 5, 5, 1 ], 514, 47, "homomorphismbyunion for groupoids",
"X847094F478113EA6" ],
[ "\033[2XIsomorphismGroupoids\033[102X", "5.5-2", [ 5, 5, 2 ], 544, 47,
"isomorphismgroupoids", "X7E2C6BCC7AAB25BE" ],
[ "\033[2XGroupoidAutomorphismByObjectPerm\033[102X", "6.1-1", [ 6, 1, 1 ],
11, 49, "groupoidautomorphismbyobjectperm", "X79DA704A8051CB72" ],
[ "\033[2XGroupoidAutomorphismByGroupAuto\033[102X", "6.1-1", [ 6, 1, 1 ],
11, 49, "groupoidautomorphismbygroupauto", "X79DA704A8051CB72" ],
[ "\033[2XGroupoidAutomorphismByNtuple\033[102X", "6.1-1", [ 6, 1, 1 ], 11,
49, "groupoidautomorphismbyntuple", "X79DA704A8051CB72" ],
[ "\033[2XGroupoidAutomorphismByRayShifts\033[102X", "6.1-1", [ 6, 1, 1 ],
11, 49, "groupoidautomorphismbyrayshifts", "X79DA704A8051CB72" ],
[ "\033[2XGroupoidInnerAutomorphism\033[102X", "6.1-2", [ 6, 1, 2 ], 122,
51, "groupoidinnerautomorphism", "X86BD61567B41B139" ],
[ "\033[2XGroupoidInnerAutomorphismNormalSubgroupoid\033[102X", "6.1-2",
[ 6, 1, 2 ], 122, 51, "groupoidinnerautomorphismnormalsubgroupoid",
"X86BD61567B41B139" ],
[ "inner automorphism", "6.1-2", [ 6, 1, 2 ], 122, 51, "inner automorphism",
"X86BD61567B41B139" ],
[ "\033[2XAutomorphismGroupOfGroupoid\033[102X", "6.1-4", [ 6, 1, 4 ], 274,
53, "automorphismgroupofgroupoid", "X7DB9D5737EB8C260" ],
[ "\033[2XNiceObjectAutoGroupGroupoid\033[102X", "6.1-4", [ 6, 1, 4 ], 274,
53, "niceobjectautogroupgroupoid", "X7DB9D5737EB8C260" ],
[ "\033[10XAutomorphismGroup\033[110X", "6.1-4", [ 6, 1, 4 ], 274, 53,
"automorphismgroup", "X7DB9D5737EB8C260" ],
[ "inner automorphism group", "6.1-5", [ 6, 1, 5 ], 323, 54,
"inner automorphism group", "X7EC237ED7E1978B0" ],
[ "\033[2XGroupoidAutomorphismByGroupAutos\033[102X", "6.1-6", [ 6, 1, 6 ],
370, 55, "groupoidautomorphismbygroupautos", "X80F9594481CA9FDE" ],
[ "\033[2XAutomorphismGroupoidOfGroupoid\033[102X", "6.1-7", [ 6, 1, 7 ],
447, 56, "automorphismgroupoidofgroupoid", "X7A93C6507BC697CD" ],
[ "matrix representation", "6.2", [ 6, 2, 0 ], 491, 57,
"matrix representation", "X8003AF117B956D16" ],
[ "representation by matrices", "6.2", [ 6, 2, 0 ], 491, 57,
"representation by matrices", "X8003AF117B956D16" ],
[ "groupoid action", "6.3", [ 6, 3, 0 ], 553, 58, "groupoid action",
"X7DB8E7EF7A51F1BE" ],
[ "conjugation identities", "6.3", [ 6, 3, 0 ], 553, 58,
"conjugation identities", "X7DB8E7EF7A51F1BE" ],
[ "\033[2XGroupoidActionByConjugation\033[102X", "6.3-1", [ 6, 3, 1 ], 614,
59, "groupoidactionbyconjugation", "X7C4DCB287B3DD0CD" ],
[ "\033[2XIsGroupoidAction\033[102X", "6.3-1", [ 6, 3, 1 ], 614, 59,
"isgroupoidaction", "X7C4DCB287B3DD0CD" ],
[ "\033[2XActionMap\033[102X", "6.3-1", [ 6, 3, 1 ], 614, 59, "actionmap",
"X7C4DCB287B3DD0CD" ],
[ "\033[2XFpWeightedDigraph\033[102X", "7.1-1", [ 7, 1, 1 ], 16, 61,
"fpweighteddigraph", "X85BD6D2584D8A22F" ],
[ "\033[2XIsFpWeightedDigraph\033[102X", "7.1-1", [ 7, 1, 1 ], 16, 61,
"isfpweighteddigraph", "X85BD6D2584D8A22F" ],
[ "\033[2XInvolutoryArcs\033[102X", "7.1-1", [ 7, 1, 1 ], 16, 61,
"involutoryarcs", "X85BD6D2584D8A22F" ],
[ "\033[2XGraphOfGroups\033[102X", "7.2-1", [ 7, 2, 1 ], 68, 62,
"graphofgroups", "X8130246E854BC5D9" ],
[ "\033[2XDigraphOfGraphOfGroups\033[102X", "7.2-1", [ 7, 2, 1 ], 68, 62,
"digraphofgraphofgroups", "X8130246E854BC5D9" ],
[ "\033[2XGroupsOfGraphOfGroups\033[102X", "7.2-1", [ 7, 2, 1 ], 68, 62,
"groupsofgraphofgroups", "X8130246E854BC5D9" ],
[ "\033[2XIsomorphismsOfGraphOfGroups\033[102X", "7.2-1", [ 7, 2, 1 ], 68,
62, "isomorphismsofgraphofgroups", "X8130246E854BC5D9" ],
[ "\033[2XIsGraphOfGroups\033[102X", "7.2-1", [ 7, 2, 1 ], 68, 62,
"isgraphofgroups", "X8130246E854BC5D9" ],
[ "\033[2XIsGraphOfFpGroups\033[102X", "7.2-2", [ 7, 2, 2 ], 142, 63,
"isgraphoffpgroups", "X847464677F641527" ],
[ "\033[2XIsGraphOfPcGroups\033[102X", "7.2-2", [ 7, 2, 2 ], 142, 63,
"isgraphofpcgroups", "X847464677F641527" ],
[ "\033[2XIsGraphOfPermGroups\033[102X", "7.2-2", [ 7, 2, 2 ], 142, 63,
"isgraphofpermgroups", "X847464677F641527" ],
[ "\033[2XRightTransversalsOfGraphOfGroups\033[102X", "7.2-3", [ 7, 2, 3 ],
162, 64, "righttransversalsofgraphofgroups", "X7B036C2B84E48BB1" ],
[ "\033[2XLeftTransversalsOfGraphOfGroups\033[102X", "7.2-3", [ 7, 2, 3 ],
162, 64, "lefttransversalsofgraphofgroups", "X7B036C2B84E48BB1" ],
[ "\033[2XGraphOfGroupsWord\033[102X", "7.3-1", [ 7, 3, 1 ], 190, 64,
"graphofgroupsword", "X87937AE47C5B1018" ],
[ "\033[2XIsGraphOfGroupsWord\033[102X", "7.3-1", [ 7, 3, 1 ], 190, 64,
"isgraphofgroupsword", "X87937AE47C5B1018" ],
[ "\033[2XGraphOfGroupsOfWord\033[102X", "7.3-1", [ 7, 3, 1 ], 190, 64,
"graphofgroupsofword", "X87937AE47C5B1018" ],
[ "\033[2XWordOfGraphOfGroupsWord\033[102X", "7.3-1", [ 7, 3, 1 ], 190, 64,
"wordofgraphofgroupsword", "X87937AE47C5B1018" ],
[ "\033[2XTailOfGraphOfGroupsWord\033[102X", "7.3-1", [ 7, 3, 1 ], 190, 64,
"tailofgraphofgroupsword", "X87937AE47C5B1018" ],
[ "\033[2XHeadOfGraphOfGroupsWord\033[102X", "7.3-1", [ 7, 3, 1 ], 190, 64,
"headofgraphofgroupsword", "X87937AE47C5B1018" ],
[ "\033[2XReducedGraphOfGroupsWord\033[102X", "7.3-2", [ 7, 3, 2 ], 239,
65, "reducedgraphofgroupsword", "X78FA7C3F831AA6E4" ],
[ "\033[2XIsReducedGraphOfGroupsWord\033[102X", "7.3-2", [ 7, 3, 2 ], 239,
65, "isreducedgraphofgroupsword", "X78FA7C3F831AA6E4" ],
[ "\033[2XFreeProductWithAmalgamation\033[102X", "7.4-1", [ 7, 4, 1 ], 276,
65, "freeproductwithamalgamation", "X795AB71F7E370119" ],
[ "\033[2XFreeProductWithAmalgamationInfo\033[102X", "7.4-1", [ 7, 4, 1 ],
276, 65, "freeproductwithamalgamationinfo", "X795AB71F7E370119" ],
[ "\033[2XIsFreeProductWithAmalgamation\033[102X", "7.4-1", [ 7, 4, 1 ],
276, 65, "isfreeproductwithamalgamation", "X795AB71F7E370119" ],
[ "\033[2XGraphOfGroupsRewritingSystem\033[102X", "7.4-1", [ 7, 4, 1 ],
276, 65, "graphofgroupsrewritingsystem", "X795AB71F7E370119" ],
[ "\033[2XNormalFormGGRWS\033[102X", "7.4-1", [ 7, 4, 1 ], 276, 65,
"normalformggrws", "X795AB71F7E370119" ],
[ "\033[2XReducedImageElm\033[102X", "7.4-2", [ 7, 4, 2 ], 348, 67,
"reducedimageelm", "X86F5F9787E3644FD" ],
[ "\033[2XIsMappingToGroupWithGGRWS\033[102X", "7.4-2", [ 7, 4, 2 ], 348,
67, "ismappingtogroupwithggrws", "X86F5F9787E3644FD" ],
[ "\033[2XEmbedding\033[102X for fpa-groups", "7.4-2", [ 7, 4, 2 ], 348,
67, "embedding for fpa-groups", "X86F5F9787E3644FD" ],
[ "\033[2XHnnExtension\033[102X", "7.4-3", [ 7, 4, 3 ], 379, 67,
"hnnextension", "X7CB0F120804A8DED" ],
[ "\033[2XHnnExtensionInfo\033[102X", "7.4-3", [ 7, 4, 3 ], 379, 67,
"hnnextensioninfo", "X7CB0F120804A8DED" ],
[ "\033[2XIsHnnExtension\033[102X", "7.4-3", [ 7, 4, 3 ], 379, 67,
"ishnnextension", "X7CB0F120804A8DED" ],
[ "\033[2XGraphOfGroupoids\033[102X", "7.5-1", [ 7, 5, 1 ], 447, 68,
"graphofgroupoids", "X8739267678808E85" ],
[ "\033[2XIsGraphOfPermGroupoids\033[102X", "7.5-1", [ 7, 5, 1 ], 447, 68,
"isgraphofpermgroupoids", "X8739267678808E85" ],
[ "\033[2XIsGraphOfFpGroupoids\033[102X", "7.5-1", [ 7, 5, 1 ], 447, 68,
"isgraphoffpgroupoids", "X8739267678808E85" ],
[ "\033[2XGroupoidsOfGraphOfGroupoids\033[102X", "7.5-1", [ 7, 5, 1 ], 447,
68, "groupoidsofgraphofgroupoids", "X8739267678808E85" ],
[ "\033[2XDigraphOfGraphOfGroupoids\033[102X", "7.5-1", [ 7, 5, 1 ], 447,
68, "digraphofgraphofgroupoids", "X8739267678808E85" ],
[ "\033[2XSubgroupoidsOfGraphOfGroupoids\033[102X", "7.5-1", [ 7, 5, 1 ],
447, 68, "subgroupoidsofgraphofgroupoids", "X8739267678808E85" ],
[ "\033[2XIsomorphismsOfGraphOfGroupoids\033[102X", "7.5-1", [ 7, 5, 1 ],
447, 68, "isomorphismsofgraphofgroupoids", "X8739267678808E85" ],
[ "\033[2XRightTransversalsOfGraphOfGroupoids\033[102X", "7.5-1",
[ 7, 5, 1 ], 447, 68, "righttransversalsofgraphofgroupoids",
"X8739267678808E85" ],
[ "\033[2XLeftTransversalsOfGraphOfGroupoids\033[102X", "7.5-1",
[ 7, 5, 1 ], 447, 68, "lefttransversalsofgraphofgroupoids",
"X8739267678808E85" ],
[ "\033[2XIsGraphOfGroupoids\033[102X", "7.5-1", [ 7, 5, 1 ], 447, 68,
"isgraphofgroupoids", "X8739267678808E85" ],
[ "\033[2XGraphOfGroupoidsWord\033[102X", "7.5-2", [ 7, 5, 2 ], 523, 70,
"graphofgroupoidsword", "X7EC1A9067FC91255" ],
[ "\033[2XIsGraphOfGroupoidsWord\033[102X", "7.5-2", [ 7, 5, 2 ], 523, 70,
"isgraphofgroupoidsword", "X7EC1A9067FC91255" ],
[ "\033[2XGraphOfGroupoidsOfWord\033[102X", "7.5-2", [ 7, 5, 2 ], 523, 70,
"graphofgroupoidsofword", "X7EC1A9067FC91255" ],
[ "\033[2XWordOfGraphOfGroupoidsWord\033[102X", "7.5-2", [ 7, 5, 2 ], 523,
70, "wordofgraphofgroupoidsword", "X7EC1A9067FC91255" ],
[ "\033[2XReducedGraphOfGroupoidsWord\033[102X", "7.5-2", [ 7, 5, 2 ], 523,
70, "reducedgraphofgroupoidsword", "X7EC1A9067FC91255" ],
[ "\033[2XIsReducedGraphOfGroupoidsWord\033[102X", "7.5-2", [ 7, 5, 2 ],
523, 70, "isreducedgraphofgroupoidsword", "X7EC1A9067FC91255" ],
[ "\033[2XSinglePieceBasicDoubleGroupoid\033[102X", "8.1-1", [ 8, 1, 1 ],
26, 72, "singlepiecebasicdoublegroupoid", "X7F5D722C83CB9139" ],
[ "\033[2XDoubleGroupoid\033[102X", "8.1-1", [ 8, 1, 1 ], 26, 72,
"doublegroupoid", "X7F5D722C83CB9139" ],
[ "\033[2XIsDoubleGroupoid\033[102X", "8.1-1", [ 8, 1, 1 ], 26, 72,
"isdoublegroupoid", "X7F5D722C83CB9139" ],
[ "\033[2XIsBasicDoubleGroupoid\033[102X", "8.1-1", [ 8, 1, 1 ], 26, 72,
"isbasicdoublegroupoid", "X7F5D722C83CB9139" ],
[ "\033[2XSquareOfArrows\033[102X", "8.1-2", [ 8, 1, 2 ], 52, 73,
"squareofarrows", "X823A3A7481B90EB7" ],
[ "\033[2XUpArrow\033[102X", "8.1-2", [ 8, 1, 2 ], 52, 73, "uparrow",
"X823A3A7481B90EB7" ],
[ "\033[2XLeftArrow\033[102X", "8.1-2", [ 8, 1, 2 ], 52, 73, "leftarrow",
"X823A3A7481B90EB7" ],
[ "\033[2XRightArrow\033[102X", "8.1-2", [ 8, 1, 2 ], 52, 73, "rightarrow",
"X823A3A7481B90EB7" ],
[ "\033[2XDownArrow\033[102X", "8.1-2", [ 8, 1, 2 ], 52, 73, "downarrow",
"X823A3A7481B90EB7" ],
[ "\033[2XBoundaryOfSquare\033[102X", "8.1-2", [ 8, 1, 2 ], 52, 73,
"boundaryofsquare", "X823A3A7481B90EB7" ],
[ "\033[2XDoubleGroupoidOfSquare\033[102X", "8.1-2", [ 8, 1, 2 ], 52, 73,
"doublegroupoidofsquare", "X823A3A7481B90EB7" ],
[ "\033[2XIsDoubleGroupoidElement\033[102X", "8.1-2", [ 8, 1, 2 ], 52, 73,
"isdoublegroupoidelement", "X823A3A7481B90EB7" ],
[ "\033[2XIsCommutingSquare\033[102X", "8.1-3", [ 8, 1, 3 ], 120, 74,
"iscommutingsquare", "X83DF8EEE7BA72AA3" ],
[ "\033[2XTransposedSquare\033[102X", "8.1-4", [ 8, 1, 4 ], 146, 74,
"transposedsquare", "X7F99A468819D7759" ],
[ "\033[2XIsClosedUnderTransposition\033[102X", "8.1-4", [ 8, 1, 4 ], 146,
74, "isclosedundertransposition", "X7F99A468819D7759" ],
[ "\033[2XHorizontalProduct\033[102X", "8.1-5", [ 8, 1, 5 ], 168, 75,
"horizontalproduct", "X7D3737FA7E9E3ECA" ],
[ "\033[2XVerticalProduct\033[102X", "8.1-6", [ 8, 1, 6 ], 212, 75,
"verticalproduct", "X873F01287A2DC41F" ],
[ "\033[2XHorizontalIdentities\033[102X", "8.1-7", [ 8, 1, 7 ], 332, 78,
"horizontalidentities", "X79E6E4E97A23C257" ],
[ "\033[2XVerticalIdentities\033[102X", "8.1-7", [ 8, 1, 7 ], 332, 78,
"verticalidentities", "X79E6E4E97A23C257" ],
[ "\033[2XHorizontalInverses\033[102X", "8.1-7", [ 8, 1, 7 ], 332, 78,
"horizontalinverses", "X79E6E4E97A23C257" ],
[ "\033[2XVerticalInverses\033[102X", "8.1-7", [ 8, 1, 7 ], 332, 78,
"verticalinverses", "X79E6E4E97A23C257" ],
[ "", "8.1-8", [ 8, 1, 8 ], 466, 80, "", "X7B8DEF5A7B5AEC46" ],
[ "", "8.1-8", [ 8, 1, 8 ], 466, 80, "", "X7B8DEF5A7B5AEC46" ],
[ "\033[2XUnionOfPieces\033[102X for double groupoids", "8.2-1",
[ 8, 2, 1 ], 495, 81, "unionofpieces for double groupoids",
"X8589EFAE7935BEA6" ],
[ "\033[2XPieces\033[102X for double groupoids", "8.2-1", [ 8, 2, 1 ], 495,
81, "pieces for double groupoids", "X8589EFAE7935BEA6" ],
[ "\033[2XDoubleGroupoidWithTrivialGroup\033[102X", "8.3-1", [ 8, 3, 1 ],
544, 82, "doublegroupoidwithtrivialgroup", "X80009143808725D5" ],
[ "\033[2XDoubleGroupoidWithSingleObject\033[102X", "8.3-2", [ 8, 3, 2 ],
570, 82, "doublegroupoidwithsingleobject", "X7D135AFB83995A32" ],
[ "\033[2XDoubleGroupoidHomomorphism\033[102X", "8.5-1", [ 8, 5, 1 ], 669,
84, "doublegroupoidhomomorphism", "X87752436787B199D" ],
[ "\033[2XIsDoubleGroupoidHomomorphism\033[102X", "8.5-1", [ 8, 5, 1 ],
669, 84, "isdoublegroupoidhomomorphism", "X87752436787B199D" ] ]
);
[ Dauer der Verarbeitung: 0.21 Sekunden
(vorverarbeitet)
]
|
