https://cattheory.subwiki.org/w/index.php?action=history&feed=atom&title=Symmetric_monoidal_categorySymmetric monoidal category - Revision history2026-05-18T16:42:27ZRevision history for this page on the wikiMediaWiki 1.41.2https://cattheory.subwiki.org/w/index.php?title=Symmetric_monoidal_category&diff=41&oldid=prevVipul: New page: {{category plus additional structure}} ==Definition== A '''symmetric monoidal category''' is a monoidal category <math>(\mathcal{C}, \otimes)</math> equipped with a commutativity iso...2008-12-09T01:56:11Z<p>New page: {{category plus additional structure}} ==Definition== A '''symmetric monoidal category''' is a <a href="/wiki/Monoidal_category" title="Monoidal category">monoidal category</a> <math>(\mathcal{C}, \otimes)</math> equipped with a commutativity iso...</p>
<p><b>New page</b></p><div>{{category plus additional structure}}<br />
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==Definition==<br />
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A '''symmetric monoidal category''' is a [[monoidal category]] <math>(\mathcal{C}, \otimes)</math> equipped with a commutativity isomorphism: for every <math>A,B \in \operatorname{Ob}\mathcal{C}</math> an isomorphism:<br />
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<math>\tau_{AB}: A \otimes B \to B \otimes A</math><br />
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such that:<br />
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* <math>\tau</math> is natural in both variables.<br />
* For any objects <math>A, B</math>, <math>\tau_{BA} \circ \tau_{AB}</math> is the identity map on <math>A \otimes B</math>.</div>Vipul