Theorems · Definition · category theory

HomologicalComplex.pathObject.homotopyEquiv

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {α : Type u_2} →
        {c : ComplexShape α} →
          (K : HomologicalComplex C c) →
            [inst_2 : DecidableRel c.Rel] →
              [inst_3 : ∀ (i : α), CategoryTheory.Limits.HasBinaryBiproduct (K.X i) (K.X i)] →
                [inst_4 : K.HasPathObject] → (∀ (i : α), ∃ j, c.Rel i j) → HomotopyEquiv K K.pathObject

The homotopy equivalence between K and K.pathObject.

Defined in

Mathlib.Algebra.Homology.HomotopyFiber

Cited by

4 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveDecidableRelCategoryTheory.Limits.HasBinaryBiproductHomologicalComplex.HasPathObject