Theorems · Theorem · category theory

CategoryTheory.Abelian.OfCoimageImageComparisonIsIso.isNormalMonoCategory

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasKernels C] [inst_3 : CategoryTheory.Limits.HasCokernels C]
  [∀ {X Y : C} (f : X ⟶ Y), CategoryTheory.IsIso (CategoryTheory.Abelian.coimageImageComparison f)]
  [CategoryTheory.Limits.HasFiniteProducts C], CategoryTheory.IsNormalMonoCategory C

A category with finite products in which coimage-image comparisons are all isomorphisms is a normal mono category.

Defined in

Mathlib.CategoryTheory.Abelian.Basic

Cited by

0 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasKernelsCategoryTheory.Limits.HasCokernelsCategoryTheory.IsIsoCategoryTheory.Limits.HasFiniteProducts