[Merged by Bors] - feat(CategoryTheory): the equivalence of categories induced by a bijection#20881
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[Merged by Bors] - feat(CategoryTheory): the equivalence of categories induced by a bijection#20881
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PR summary 1c8cca8aa6Import changes for modified filesNo significant changes to the import graph Import changes for all files
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…ction (#20881) When `f : T → D` is a map and `D` is a category, then `InducedCategory D f` is a category with objects `T` with a fully faithful functor to `D`. In this PR, we show that in the case of a bijection `T ≃ D`, the induced category is equivalent to `D`. The code would be nicer (see #19945) if the type of morphisms in the induced category was defined as a 1-field structure. This would be a very welcomed refactor.
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When
f : T → Dis a map andDis a category, thenInducedCategory D fis a category with objectsTwith a fully faithful functor toD. In this PR, we show that in the case of a bijectionT ≃ D, the induced category is equivalent toD.The code would be nicer (see #19945) if the type of morphisms in the induced category was defined as a 1-field structure. This would be a very welcomed refactor.