Theorems · Inductive type · category theory
CategoryTheory.Functor.IsIso
{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] → CategoryTheory.Functor C D → PropA functor F : C ⥤ D is an isomorphism of categories if it is full, faithful and
bijective on objects. Such a functor has a strict inverse Functor.strictInv and assembles
into an IsoCat via Functor.asIsomorphism.
- Defined in
- Mathlib.CategoryTheory.IsoCat
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.objEquivstatement and proof · cited by 3
- CategoryTheory.Functor.objEquiv_apply_symm_applystatement and proof · cited by 0
- CategoryTheory.Functor.objEquiv_symm_apply_applystatement and proof · cited by 0
- CategoryTheory.Functor.asIsomorphismstatement and proof · cited by 0
- CategoryTheory.Functor.IsIso.bijective_objstatement and proof · cited by 0
- CategoryTheory.Functor.IsIso.casesOnstatement and proof · cited by 0
- CategoryTheory.Functor.IsIso.recOnstatement and proof · cited by 0
- CategoryTheory.Functor.strictInvstatement and proof · cited by 0
- CategoryTheory.Functor.objEquiv.congr_simpstatement and proof · cited by 0