Theorems · Theorem · category theory

HomologicalComplex.extend.d_eq

∀ {ι : Type u_1} {c : ComplexShape ι} {C : Type u_3} [inst : CategoryTheory.Category.{v_1, u_3} C]
  [inst_1 : CategoryTheory.Limits.HasZeroObject C] [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C]
  (K : HomologicalComplex C c) {i j : Option ι} {a b : ι} (hi : i = some a) (hj : j = some b),
  HomologicalComplex.extend.d K i j =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.extend.XIso K hi).hom
      (CategoryTheory.CategoryStruct.comp (K.d a b) (HomologicalComplex.extend.XIso K hj).inv)

Defined in

Mathlib.Algebra.Homology.Embedding.Extend

Cited by

2 results in Mathlib

Foundations

Depth 13 from the axioms · uses propext, Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms