Theorems · Theorem · category theory

HomologicalComplex.extend.mapX_some

∀ {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 L : HomologicalComplex C c} (φ : K ⟶ L) {i : Option ι} {a : ι} (hi : i = some a),
  HomologicalComplex.extend.mapX φ i =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.extend.XIso K hi).hom
      (CategoryTheory.CategoryStruct.comp (φ.f a) (HomologicalComplex.extend.XIso L hi).inv)

Defined in

Mathlib.Algebra.Homology.Embedding.Extend

Cited by

1 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms