Theorems · Theorem · category theory

HomologicalComplex.stupidTruncMap_stupidTruncXIso_hom_assoc

∀ {ι : Type u_1} {ι' : Type u_2} {c : ComplexShape ι} {c' : ComplexShape ι'} {C : Type u_3}
  [inst : CategoryTheory.Category.{v_1, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] {K L : HomologicalComplex C c'} (φ : K ⟶ L) (e : c.Embedding c')
  [inst_3 : e.IsRelIff] {i : ι} {i' : ι'} (hi : e.f i = i') {Z : C} (h : L.X i' ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((HomologicalComplex.stupidTruncMap φ e).f i')
      (CategoryTheory.CategoryStruct.comp (L.stupidTruncXIso e hi).hom h) =
    CategoryTheory.CategoryStruct.comp (K.stupidTruncXIso e hi).hom (CategoryTheory.CategoryStruct.comp (φ.f i') h)

Defined in

Mathlib.Algebra.Homology.Embedding.StupidTrunc

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectComplexShape.Embedding.IsRelIff