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<p><a id="X7BAE6D0285667B1F" name="X7BAE6D0285667B1F"></a></p>
<div class="ChapSects"><a href="chap16_mj.html#X7BAE6D0285667B1F">16 <span class="Heading">Finite skeletal discrete categories</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap16_mj.html#X7D03633A7D98026B">16.1 <span class="Heading"><strong class="pkg">GAP</strong> Categories</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap16_mj.html#X86FECC7F7B10DFB5">16.1-1 IsFiniteSkeletalDiscreteCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap16_mj.html#X7B0369367B25FF27">16.1-2 IsObjectInFiniteSkeletalDiscreteCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap16_mj.html#X83A994137F28C142">16.1-3 IsMorphismInFiniteSkeletalDiscreteCategory</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap16_mj.html#X86EC0F0A78ECBC10">16.2 <span class="Heading">Constructors</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap16_mj.html#X82D81EB281E4B15F">16.2-1 FiniteSkeletalDiscreteCategory</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap16_mj.html#X7C701DBF7BAE649A">16.3 <span class="Heading">Attributes</span></a>
</span>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap16_mj.html#X82A86530836AB45F">16.3-1 UnderlyingListOfGapObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap16_mj.html#X83402D288247887B">16.3-2 UnderlyingGapObject</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap16_mj.html#X871597447BB998A1">16.4 <span class="Heading">Properties</span></a>
</span>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap16_mj.html#X7F7BD8CF86A2D122">16.4-1 IsDiscreteCategory</a></span>
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<h3>16 <span class="Heading">Finite skeletal discrete categories</span></h3>

<p><a id="X7D03633A7D98026B" name="X7D03633A7D98026B"></a></p>

<h4>16.1 <span class="Heading"><strong class="pkg">GAP</strong> Categories</span></h4>

<p><a id="X86FECC7F7B10DFB5" name="X86FECC7F7B10DFB5"></a></p>

<h5>16.1-1 IsFiniteSkeletalDiscreteCategory</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsFiniteSkeletalDiscreteCategory</code>( <var class="Arg">C</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The <strong class="pkg">GAP</strong> type of a finite skeletal discrete category.</p>

<p><a id="X7B0369367B25FF27" name="X7B0369367B25FF27"></a></p>

<h5>16.1-2 IsObjectInFiniteSkeletalDiscreteCategory</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsObjectInFiniteSkeletalDiscreteCategory</code>( <var class="Arg">O</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The <strong class="pkg">GAP</strong> type of an object in a finite skeletal discrete category.</p>

<p><a id="X83A994137F28C142" name="X83A994137F28C142"></a></p>

<h5>16.1-3 IsMorphismInFiniteSkeletalDiscreteCategory</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsMorphismInFiniteSkeletalDiscreteCategory</code>( <var class="Arg">M</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The <strong class="pkg">GAP</strong> type of a morphism in a finite skeletal discrete category.</p>

<p><a id="X86EC0F0A78ECBC10" name="X86EC0F0A78ECBC10"></a></p>

<h4>16.2 <span class="Heading">Constructors</span></h4>

<p><a id="X82D81EB281E4B15F" name="X82D81EB281E4B15F"></a></p>

<h5>16.2-1 FiniteSkeletalDiscreteCategory</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; FiniteSkeletalDiscreteCategory</code>( <var class="Arg">arg</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a <strong class="pkg">CAP</strong> category</p>

<p>Construct a finite skeletal discrete category.</p>

<p><a id="X7C701DBF7BAE649A" name="X7C701DBF7BAE649A"></a></p>

<h4>16.3 <span class="Heading">Attributes</span></h4>

<p><a id="X82A86530836AB45F" name="X82A86530836AB45F"></a></p>

<h5>16.3-1 UnderlyingListOfGapObjects</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; UnderlyingListOfGapObjects</code>( <var class="Arg">arg</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a list of <strong class="pkg">CAP</strong> objects</p>

<p>The underlying <strong class="pkg">GAP</strong> objects of a finite skeletal discrete category.</p>

<p><a id="X83402D288247887B" name="X83402D288247887B"></a></p>

<h5>16.3-2 UnderlyingGapObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; UnderlyingGapObject</code>( <var class="Arg">arg</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">CAP</strong> object</p>

<p>The underlying <strong class="pkg">GAP</strong> object of an object in a finite skeletal discrete category.</p>

<p><a id="X871597447BB998A1" name="X871597447BB998A1"></a></p>

<h4>16.4 <span class="Heading">Properties</span></h4>

<p><a id="X7F7BD8CF86A2D122" name="X7F7BD8CF86A2D122"></a></p>

<h5>16.4-1 IsDiscreteCategory</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsDiscreteCategory</code>( <var class="Arg">C</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The property of <var class="Arg">C</var> being a discrete <strong class="pkg">CAP</strong> category, i.e., equivalent to a category in which any morphism is an identity.</p>


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