Theorems · Theorem · category theory

CategoryTheory.NormalMonoCategory.epi_of_zero_cokernel

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [CategoryTheory.Limits.HasFiniteProducts C] [CategoryTheory.Limits.HasKernels C]
  [CategoryTheory.IsNormalMonoCategory C] {X Y : C} (f : X ⟶ Y) (Z : C)
  (l : CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.CokernelCofork.ofπ 0 ⋯)), CategoryTheory.Epi f

If a zero morphism is a cokernel of f, then f is an epimorphism.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers

Cited by

2 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasKernelsCategoryTheory.IsNormalMonoCategory