Theorems · Definition · category theory

HomotopyEquiv.homotopyInvHomId

{ι : Type u_1} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Preadditive V] →
        {c : ComplexShape ι} →
          {C D : HomologicalComplex V c} →
            (self : HomotopyEquiv C D) →
              Homotopy (CategoryTheory.CategoryStruct.comp self.inv self.hom) (CategoryTheory.CategoryStruct.id D)

A homotopy showing that composing the backward and forward maps is homotopic to the identity on D

Defined in

Mathlib.Algebra.Homology.Homotopy

Cited by

10 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive