Theorems · Theorem · category theory

HomologicalComplex.single_map_f_self

∀ {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),
  ((HomologicalComplex.single V c j).map f).f j =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.singleObjXSelf c j A).hom
      (CategoryTheory.CategoryStruct.comp f (HomologicalComplex.singleObjXSelf c j B).inv)

Defined in

Mathlib.Algebra.Homology.Single

Cited by

7 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEq