Theorems · Theorem · algebraic topology

AlgebraicTopology.DoldKan.HigherFacesVanish.induction

∀ {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 →
    AlgebraicTopology.DoldKan.HigherFacesVanish (q + 1)
      (CategoryTheory.CategoryStruct.comp φ
        ((CategoryTheory.CategoryStruct.id (AlgebraicTopology.AlternatingFaceMapComplex.obj X) +
              AlgebraicTopology.DoldKan.Hσ q).f
          (n + 1)))

Defined in

Mathlib.AlgebraicTopology.DoldKan.Faces

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive