Theorems · Theorem · category theory

HomologicalComplex.singleObjCyclesSelfIso_hom_singleObjOpcyclesSelfIso_hom

∀ {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 : C),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.singleObjCyclesSelfIso c j A).hom
      (HomologicalComplex.singleObjOpcyclesSelfIso c j A).hom =
    CategoryTheory.CategoryStruct.comp (((HomologicalComplex.single C c j).obj A).iCycles j)
      (((HomologicalComplex.single C c j).obj A).pOpcycles j)

Defined in

Mathlib.Algebra.Homology.SingleHomology

Cited by

2 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEq