Theorems · Inductive type · category theory

CategoryTheory.Functor.ReflectsIsomorphisms

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D : Type u_2} → [inst_1 : CategoryTheory.Category.{v_2, u_2} D] → CategoryTheory.Functor C D → Prop

Define what it means for a functor F : C ⥤ D to reflect isomorphisms: for any morphism f : A ⟶ B, if F.map f is an isomorphism then f is as well. Note that we do not assume or require that F is faithful.

Defined in

Mathlib.CategoryTheory.Functor.ReflectsIso.Basic

Cited by

82 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category