Theorems · Theorem · category theory

HomologicalComplex.singleMapHomologicalComplex_inv_app_self

∀ {ι : Type u_1} {W₁ : Type u_3} {W₂ : Type u_4} [inst : CategoryTheory.Category.{v_2, u_3} W₁]
  [inst_1 : CategoryTheory.Category.{v_3, u_4} W₂] [inst_2 : CategoryTheory.Limits.HasZeroMorphisms W₁]
  [inst_3 : CategoryTheory.Limits.HasZeroMorphisms W₂] [inst_4 : CategoryTheory.Limits.HasZeroObject W₁]
  [inst_5 : CategoryTheory.Limits.HasZeroObject W₂] (F : CategoryTheory.Functor W₁ W₂)
  [inst_6 : F.PreservesZeroMorphisms] (c : ComplexShape ι) [inst_7 : DecidableEq ι] (j : ι) (X : W₁),
  ((HomologicalComplex.singleMapHomologicalComplex F c j).inv.app X).f j =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.singleObjXSelf c j (F.obj X)).hom
      (F.map (HomologicalComplex.singleObjXSelf c j X).inv)

Defined in

Mathlib.Algebra.Homology.Additive

Cited by

0 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroObjectCategoryTheory.Functor.PreservesZeroMorphismsDecidableEq