category-theory-presentation/categories/20_What/220_Isomorph.html
2013-02-28 16:49:12 +01:00

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<h2 id="isomorph">Isomorph</h2>
<p><img class="right" alt="isomorph cats" src="categories/img/isomorph-cats.jpg" /> <em class="yellow">isomorphism</em>: \(f:A→B\) which can be &quot;undone&quot; <em>i.e.</em><br />\(∃g:B→A\), \(g∘f=id_A\) &amp; \(f∘g=id_B\)<br />in this case, \(A\) &amp; \(B\) are <em class="yellow">isomorphic</em>.</p>
<p><span class="yellow">A≌B</span> means A and B are essentially the same.<br />In Category Theory, <span class="yellow">=</span> is in fact mostly <span class="yellow"></span>.<br />For example in commutative diagrams.</p>