Theorems · Theorem · category theory

CategoryTheory.ProjectiveResolution.lift_commutes

∀ {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),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.ProjectiveResolution.lift f P Q) Q.π =
    CategoryTheory.CategoryStruct.comp P.π ((ChainComplex.single₀ C).map f)

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

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Resolution

Cited by

5 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian