Theorems · Theorem · category theory

CategoryTheory.exact_d_f

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

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Resolution

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.EnoughProjectives