Theorems · Theorem · algebraic topology

AlgebraicTopology.DoldKan.HigherFacesVanish.of_P

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {X : CategoryTheory.SimplicialObject C} (q n : ℕ),
  AlgebraicTopology.DoldKan.HigherFacesVanish q ((AlgebraicTopology.DoldKan.P q).f (n + 1))

This lemma expresses the vanishing of (P q).f (n+1) ≫ X.δ k : X _⦋n+1⦌ ⟶ X _⦋n⦌ when k≠0 and k≥n-q+2

Defined in

Mathlib.AlgebraicTopology.DoldKan.Projections

Cited by

7 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive