<p>Serre quotients are implemented using generalized morphisms. A Serre quotient category is the quotient of an abelian category A by a thick subcategory C. The objects of the quotient are the objects from A, the morphisms are a limit construction. In the implementation those morphisms are modeled by generalized morphisms, and therefore there are, like in the generalized morphism case, three types of Serre quotients.</p>
<p>As in the generalized morphism case, the generic constructors depend on the generalized morphism standard. Please note that for implementations the specialized constructors should be used.</p>
<p>Creates a Serre quotient category <var class="Arg">S</var> with name <var class="Arg">name</var> out of an Abelian category <var class="Arg">A</var>. If <var class="Arg">name</var> is not given, a generic name is constructed out of the name of <var class="Arg">A</var>. The argument <var class="Arg">func</var> must be a unary function on the objects of <var class="Arg">A</var> deciding the membership in the thick subcategory C mentioned above.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> and an object <var class="Arg">M</var> in <var class="Arg">A</var>, this constructor returns the corresponding object in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> and a generalized morphism <var class="Arg">phi</var> in the generalized morphism category <var class="Arg">A/C</var> is modeled upon, this constructor returns the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> and three morphisms <span class="Math">\iota: M' \rightarrow M, \phi: M' \rightarrow N' and \pi: N \rightarrow N'</span> this operation contructs a morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> and two morphisms of the form <span class="Math">\alpha: X \rightarrow M</span> and <span class="Math">\beta: X \rightarrow N</span> or <span class="Math">\alpha: M \rightarrow X</span> and <span class="Math">\beta: N \rightarrow X</span>, this operation constructs the corresponding morphism in the Serre quotient category. This operation is only implemented if <var class="Arg">A/C</var> is modeled upon a span generalized morphism category in the first option or upon a cospan category in the second.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> and two morphisms <span class="Math">\alpha: M \rightarrow X</span> and <span class="Math">\beta: X \rightarrow N</span> this operation constructs the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> and two morphisms <span class="Math">\alpha: X \rightarrow M</span> and <span class="Math">\beta: X \rightarrow N</span> this operation constructs the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> and a morphism <var class="Arg">phi</var> in <var class="Arg">A</var>, this constructor returns the corresponding morphism in the Serre quotient category.</p>
<p>For an object <var class="Arg">M</var> in the Serre quotient category A/C this attribute returns the corresponding object in the generalized morphism category the quotient is modelled upon.</p>
<p>For an object <var class="Arg">M</var> in the Serre quotient category A/C this attribute returns the corresponding object in <var class="Arg">A</var>.</p>
<p>For a morphism <var class="Arg">phi</var> in the Serre quotient category A/C this attribute returns the corresponding generalized morphism in the generalized morphism category the quotient is modelled upon.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var>, this operation returns the canonical projection functor <span class="Math"> A \rightarrow A/C </span>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SerreQuotientCategoryByCospans</code>( <var class="Arg">A</var>, <var class="Arg">func</var>[, <varclass="Arg">name</var>] )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a CAP category</p>
<p>Creates a Serre quotient category S with name <var class="Arg">name</var> out of an Abelian category <var class="Arg">A</var>. The Serre quotient category will be modeled upon the generalized morphisms by cospans category of <var class="Arg">A</var> If <var class="Arg">name</var> is not given, a generic name is constructed out of the name of <var class="Arg">A</var>. The argument <var class="Arg">func</var> must be a unary function on the objects of <var class="Arg">A</var> deciding the membership in the thick subcategory C mentioned above.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by cospans and an object <var class="Arg">M</var> in <var class="Arg">A</var>, this constructor returns the corresponding objectin the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by cospans and a generalized morphism <var class="Arg">phi</var> in the generalized morphism category <var class="Arg">A/C</var> is modeled upon, this constructor returns the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by cospans and three morphisms <span class="Math">\iota: M' \rightarrow M, \phi: M' \rightarrow N' and \pi: N \rightarrow N'</span> this operation contructs a morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by cospans and two morphisms <span class="Math">\alpha: M \rightarrow X</span> and <span class="Math">\beta: X \rightarrow N</span> this operation constructs the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by cospans and two morphisms <span class="Math">\alpha: X \rightarrow M</span> and <span class="Math">\beta: X \rightarrow N</span> this operation constructs the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by cospans and a morphism <varclass="Arg">phi</var> in <var class="Arg">A</var>, this constructor returns the corresponding morphism in the Serre quotient category.</p>
<p>Creates a Serre quotient category S with name <var class="Arg">name</var> out of an Abelian category <var class="Arg">A</var>. The Serre quotient category will be modeled upon the generalized morphisms by spans category of <var class="Arg">A</var> If <var class="Arg">name</var> is not given, a generic name is constructed out of the name of <var class="Arg">A</var>. The argument <var class="Arg">func</var> must be a unary function on the objects of <var class="Arg">A</var> deciding the membership in the thick subcategory C mentioned above.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by spans and an object <var class="Arg">M</var> in <var class="Arg">A</var>, this constructor returns the corresponding object in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by spans and a generalized morphism <var class="Arg">phi</var> in the generalized morphism category <var class="Arg">A/C</var> is modeled upon, this constructor returns the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by spans and three morphisms <span class="Math">\iota: M' \rightarrow M, \phi: M' \rightarrow N' and \pi: N \rightarrow N'</span> this operation contructs a morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by spans and two morphisms <span class="Math">\alpha: M \rightarrow X</span> and <span class="Math">\beta: X \rightarrow N</span> this operation constructs the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by spans and two morphisms <span class="Math">\alpha: X \rightarrow M</span> and <span class="Math">\beta: X \rightarrow N</span> this operation constructs the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by spans and a morphism <var class="Arg">phi</var> in <var class="Arg">A</var>, this constructor returns the corresponding morphism in the Serre quotient category.</p>
<p>Creates a Serre quotient category S with name <var class="Arg">name</var> out of an Abelian category <var class="Arg">A</var>. The Serre quotient category will be modeled upon the generalized morphisms by three arrows category of <var class="Arg">A</var> If <var class="Arg">name</var> is not given, a generic name is constructed out of the name of <var class="Arg">A</var>. The argument <var class="Arg">func</var> must be a unary function on the objects of <var class="Arg">A</var> deciding the membership in the thick subcategory C mentioned above.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by three arrows and an object <var class="Arg">M</var> in <var class="Arg">A</var>, this constructor returns the corresponding object in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by three arrows and a generalized morphism <var class="Arg">phi</var> in the generalized morphism category <var class="Arg">A/C</var> is modeled upon, this constructor returns the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by three arrows and three morphisms <span class="Math">\iota: M' \rightarrow M, \phi: M' \rightarrow N' and \pi: N \rightarrow N'</span> this operation contructs a morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by three arrows and two morphisms <span class="Math">\alpha: M \rightarrow X</span> and <span class="Math">\beta: X \rightarrow N</span> this operation constructs the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by three arrows and two morphisms <span class="Math">\alpha: X \rightarrow M</span> and <span class="Math">\beta: X \rightarrow N</span> this operation constructs the corresponding morphism in the Serre quotient category.</p>
<p>Given a Serre quotient category <var class="Arg">A/C</var> modeled by three arrows and a morphism <var class="Arg">phi</var> in <var class="Arg">A</var>, this constructor returns the corresponding morphism in the Serre quotient category.</p>
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