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  "body": "\n## Summary\n\nA bicategory is a weak form of a [[2-category|CQACXG10JZ]]: composition of 1-morphisms is associative and unital only up to specified invertible 2-morphisms.\nThese associators and unitors must satisfy the pentagon and triangle identities, as in a [[monoidal category|M3MSQ3NKAE]].\nA bicategory with one object is the same as a monoidal category.\nRings with bimodules, and categories with [[profunctors|EAPHAQVVD5]], form bicategories that are not strict 2-categories.\n\n## Explanations\n\n### L1 human\n\nIn many examples, composing arrows in two different orders gives results that are naturally isomorphic but not literally equal.\nTensoring bimodules is the typical case: $(M \\otimes N) \\otimes P$ and $M \\otimes (N \\otimes P)$ are isomorphic, not the same.\nA bicategory keeps track of these isomorphisms as part of the structure, instead of pretending they are equalities.\nEvery bicategory is equivalent to a strict 2-category, so not much is lost, but the weak version is the one that occurs in nature.\n",
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