Theorems · Theorem · category theory

HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturality_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] {ι : Type u_1} [inst_3 : DecidableEq ι] (c : ComplexShape ι) (j : ι)
  {A B : C} (f : A ⟶ B) {Z : C} (h : ((HomologicalComplex.single C c j).obj B).opcycles j ⟶ Z),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.singleObjOpcyclesSelfIso c j A).hom
      (CategoryTheory.CategoryStruct.comp (HomologicalComplex.opcyclesMap ((HomologicalComplex.single C c j).map f) j)
        h) =
    CategoryTheory.CategoryStruct.comp f
      (CategoryTheory.CategoryStruct.comp (HomologicalComplex.singleObjOpcyclesSelfIso c j B).hom h)

Defined in

Mathlib.Algebra.Homology.SingleHomology

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEq