Theorems · Theorem · category theory

ComplexShape.Embedding.homRestrict.comm

∀ {ι : Type u_1} {ι' : Type u_2} {c : ComplexShape ι} {c' : ComplexShape ι'} {e : c.Embedding c'} {C : Type u_3}
  [inst : CategoryTheory.Category.{v_1, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] {K : HomologicalComplex C c'} {L : HomologicalComplex C c}
  [inst_3 : e.IsRelIff] (ψ : K ⟶ L.extend e) (i j : ι),
  CategoryTheory.CategoryStruct.comp (ComplexShape.Embedding.homRestrict.f ψ i) (L.d i j) =
    CategoryTheory.CategoryStruct.comp (K.d (e.f i) (e.f j)) (ComplexShape.Embedding.homRestrict.f ψ j)

Defined in

Mathlib.Algebra.Homology.Embedding.HomEquiv

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectComplexShape.Embedding.IsRelIff