Theorems · Theorem · category theory

CategoryTheory.exact_f_d

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.EnoughInjectives C] {X Y : C} (f : X ⟶ Y),
  { X₁ := X, X₂ := Y, X₃ := CategoryTheory.Injective.syzygies f, f := f, g := CategoryTheory.Injective.d f,
      zero := ⋯ }.Exact

Defined in

Mathlib.CategoryTheory.Abelian.Injective.Resolution

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.EnoughInjectives