Theorems · Definition · category theory

CategoryTheory.Functor.objEquiv

{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) → [F.IsIso] → C ≃ D

The bijection on objects induced by a functor that is an isomorphism of categories.

Defined in: Mathlib.CategoryTheory.IsoCat
Cited by: 3 results in Mathlib
Foundations: Depth 13 from the axioms · uses Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.IsIso

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Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
Equivstatement · cited by 8,337
Equiv.ofBijectiveproof · cited by 70
CategoryTheory.Functor.IsIsostatement and proof · cited by 4
CategoryTheory.Functor.IsIso.bijective_objproof · cited by 0

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.objEquiv.congr_simpstatement and proof · cited by 0
CategoryTheory.Functor.strictInvproof · cited by 0
CategoryTheory.Functor.objEquiv_apply_symm_applystatement and proof · cited by 0
CategoryTheory.Functor.objEquiv_symm_apply_applystatement and proof · cited by 0