Theorems · Theorem · category theory

HomologicalComplex.mkHomToSingle_f

∀ {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}
  {K : HomologicalComplex V c} {j : ι} {A : V} (φ : K.X j ⟶ A)
  (hφ : ∀ (i : ι), c.Rel i j → CategoryTheory.CategoryStruct.comp (K.d i j) φ = 0),
  (HomologicalComplex.mkHomToSingle φ hφ).f j =
    CategoryTheory.CategoryStruct.comp φ (HomologicalComplex.singleObjXSelf c j A).inv

Defined in

Mathlib.Algebra.Homology.Single

Cited by

6 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEq