Theorems · Theorem · category theory

ComplexShape.Embedding.homRestrict_comp_extendMap_assoc

∀ {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 L' : HomologicalComplex C c}
  [inst_3 : e.IsRelIff] (ψ : K ⟶ L.extend e) (β : L ⟶ L') {Z : HomologicalComplex C c} (h : L' ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (e.homRestrict (CategoryTheory.CategoryStruct.comp ψ (HomologicalComplex.extendMap β e))) h =
    CategoryTheory.CategoryStruct.comp (e.homRestrict ψ) (CategoryTheory.CategoryStruct.comp β h)

Defined in

Mathlib.Algebra.Homology.Embedding.HomEquiv

Cited by

0 results in Mathlib

Foundations

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

Assumes

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