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Theorems · Theorem · category theory

CategoryTheory.Functor.IsIso.bijective_obj

∀ {C : Type u_1} {D : Type u_2} {inst : CategoryTheory.Category.{v_1, u_1} C}
  {inst_1 : CategoryTheory.Category.{v_2, u_2} D} (F : CategoryTheory.Functor C D) [self : F.IsIso],
  Function.Bijective F.obj

A functor which is an isomorphism of categories is bijective on objects.

Defined in
Mathlib.CategoryTheory.IsoCat
Cited by
0 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CategoryTheory.Functor.IsIso
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Around this declaration

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CategoryTheory.Functor.objEquiv · cited by 3Functor.objEquivCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorFunction.Bijective · cited by 863Function.BijectiveCategoryTheory.Functor.IsIso · cited by 4Functor.IsIsoIsIso.bijective_objCITED BYCITES

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Cited by1

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