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  "body": "\n## Summary\n\nA rigid monoidal category, also called an autonomous category, is a [[monoidal category|M3MSQ3NKAE]] in which every object has a left and a right [[dual object|8A7YXMW727]].\nThe main example is the category of finite-dimensional vector spaces, and more generally of finite-dimensional representations of a group.\nRigidity gives every morphism a transpose, and in the braided case it allows traces and dimensions.\nFusion categories and Tannakian categories are rigid by definition.\n\n## Explanations\n\n### L1 human\n\nEvery finite-dimensional vector space has a dual space, and every linear map has a transpose between the duals.\nA rigid monoidal category is one where every object has such a dual.\nIn string diagrams, this means that every string can be bent up or down, turning inputs into outputs.\nInfinite-dimensional vector spaces spoil this, so the category of all vector spaces is not rigid.\n",
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