Theorems · Definition · algebraic topology

AlgebraicTopology.DoldKan.homotopyPToId

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      (X : CategoryTheory.SimplicialObject C) →
        (q : ℕ) →
          Homotopy (AlgebraicTopology.DoldKan.P q)
            (CategoryTheory.CategoryStruct.id (AlgebraicTopology.AlternatingFaceMapComplex.obj X))

Inductive construction of homotopies from P q to 𝟙 _

Defined in

Mathlib.AlgebraicTopology.DoldKan.HomotopyEquivalence

Cited by

3 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive