Theorems · Theorem · category theory

HomologicalComplex.single_map_f_self_assoc

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

Defined in

Mathlib.Algebra.Homology.Single

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEq