Theorems · Theorem · category theory

HomologicalComplex.extendMap_f

∀ {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.Limits.HasZeroMorphisms C] {K L : HomologicalComplex C c} (φ : K ⟶ L) (e : c.Embedding c')
  {i : ι} {i' : ι'} (h : e.f i = i'),
  (HomologicalComplex.extendMap φ e).f i' =
    CategoryTheory.CategoryStruct.comp (K.extendXIso e h).hom
      (CategoryTheory.CategoryStruct.comp (φ.f i) (L.extendXIso e h).inv)

Defined in

Mathlib.Algebra.Homology.Embedding.Extend

Cited by

11 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms