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} (e : c.Embedding c')
  (φ : (i j : ι) → K.X i ⟶ L.X j) {i' j' : ι'} {i j : ι} (hi : e.f i = i') (hj : e.f j = j'),
  Homotopy.extend.hom e φ i' j' =
    CategoryTheory.CategoryStruct.comp (K.extendXIso e hi).hom
      (CategoryTheory.CategoryStruct.comp (φ i j) (L.extendXIso e hj).inv)

Defined in

Mathlib.Algebra.Homology.Embedding.ExtendHomotopy

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Preadditive