Theorems · Theorem · category theory

HomologicalComplex.Hom.comm_to_apply

∀ {ι : Type u_1} {V : Type u} [inst : CategoryTheory.Category.{v, u} V]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {c : ComplexShape ι} {C₁ C₂ : HomologicalComplex V c}
  (f : C₁.Hom C₂) (j : ι) {F : V → V → Type uF} {carrier : V → Type w}
  {instFunLike : (X Y : V) → FunLike (F X Y) (carrier X) (carrier Y)} [inst_2 : CategoryTheory.ConcreteCategory V F]
  (x : carrier (C₁.xPrev j)),
  (CategoryTheory.ConcreteCategory.hom (C₂.dTo j)) ((CategoryTheory.ConcreteCategory.hom (f.prev j)) x) =
    (CategoryTheory.ConcreteCategory.hom (f.f j)) ((CategoryTheory.ConcreteCategory.hom (C₁.dTo j)) x)

Defined in

Mathlib.Algebra.Homology.HomologicalComplex

Cited by

0 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ConcreteCategory