Theorems · Theorem · category theory

CategoryTheory.Abelian.tfae_mono

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Abelian C] {X Y : C} (f : X ⟶ Y)
  (Z : C),
  [CategoryTheory.Mono f, CategoryTheory.Limits.kernel.ι f = 0,
      { X₁ := Z, X₂ := X, X₃ := Y, f := 0, g := f, 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