Theorems · Theorem · category theory

HomologicalComplex.homotopyEquivalences_extendMap_iff

∀ {ι : Type u_1} {ι' : Type u_2} {c : ComplexShape ι} {c' : ComplexShape ι'} {C : Type u_3}
  [inst : CategoryTheory.Category.{v_1, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.Preadditive C] {K L : HomologicalComplex C c} (f : K ⟶ L) (e : c.Embedding c') [e.IsRelIff],
  HomologicalComplex.homotopyEquivalences C c' (HomologicalComplex.extendMap f e) ↔
    HomologicalComplex.homotopyEquivalences C c f

Defined in

Mathlib.Algebra.Homology.Embedding.ExtendHomotopy

Cited by

2 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.PreadditiveComplexShape.Embedding.IsRelIff