Theorems · Theorem · category theory

CategoryTheory.Abelian.tfae_epi

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Abelian C] {X Y : C} (f : X ⟶ Y)
  (Z : C),
  [CategoryTheory.Epi f, CategoryTheory.Limits.cokernel.π f = 0,
      { X₁ := X, X₂ := Y, X₃ := Z, f := f, g := 0, zero := ⋯ }.Exact].TFAE

Defined in

Mathlib.CategoryTheory.Abelian.Exact

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian