Theorems · Theorem · category theory

CategoryTheory.ProjectiveResolution.lift_commutes_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {Y Z : C} (f : Y ⟶ Z)
  (P : CategoryTheory.ProjectiveResolution Y) (Q : CategoryTheory.ProjectiveResolution Z) {Z_1 : ChainComplex C ℕ}
  (h : (ChainComplex.single₀ C).obj Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.ProjectiveResolution.lift f P Q)
      (CategoryTheory.CategoryStruct.comp Q.π h) =
    CategoryTheory.CategoryStruct.comp P.π (CategoryTheory.CategoryStruct.comp ((ChainComplex.single₀ C).map f) h)

The resolution maps intertwine the lift of a morphism and that morphism.

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Resolution

Cited by

0 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian