Theorems · Theorem · category theory

Homotopy.extend_hom_eq

∀ {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 g : K ⟶ L} (h : Homotopy f g)
  (e : c.Embedding c') [inst_3 : e.IsRelIff] {i' j' : ι'} {i j : ι} (hi : e.f i = i') (hj : e.f j = j'),
  (h.extend e).hom i' j' =
    CategoryTheory.CategoryStruct.comp (K.extendXIso e hi).hom
      (CategoryTheory.CategoryStruct.comp (h.hom i j) (L.extendXIso e hj).inv)

Defined in

Mathlib.Algebra.Homology.Embedding.ExtendHomotopy

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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