Commit 2025-05-20 14:06 0411276d
View on Github →feat(CategoryTheory/Equivalence): functoriality of symmetry of equivalences (#23198)
We introduce a file CategoryTheory/Equivalence/Symmetry
in which we continue to provide basic API for the category structure on equivalences defined in #23197. We prove that symmetry of equivalences defines an equivalence (C ≌ D) ≌ (D ≌ C)ᵒᵖ
, and we use this to construct Equivalence.inverseFunctor: (C ≌ D) ⥤ (D ⥤ C)ᵒᵖ
that takes an equivalence to its inverse functor, and to promote Equivalence.congrLeft
to a functor.