Theorems · Theorem · algebraic topology

AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {X : CategoryTheory.SimplicialObject C} {Y : C} {n q : ℕ} {φ : Y ⟶ X.obj (Opposite.op { len := n + 1 })},
  AlgebraicTopology.DoldKan.HigherFacesVanish q φ →
    ∀ {Z : C} (h : (AlgebraicTopology.AlternatingFaceMapComplex.obj X).X (n + 1) ⟶ Z),
      CategoryTheory.CategoryStruct.comp φ
          (CategoryTheory.CategoryStruct.comp ((AlgebraicTopology.DoldKan.P q).f (n + 1)) h) =
        CategoryTheory.CategoryStruct.comp φ h

Defined in

Mathlib.AlgebraicTopology.DoldKan.Projections

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive