Theorems · Theorem · category theory

HomologicalComplex.extendMap_comp_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.HasZeroObject C]
  [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] {K L M : HomologicalComplex C c} (φ : K ⟶ L) (φ' : L ⟶ M)
  (e : c.Embedding c') {Z : HomologicalComplex C c'} (h : M.extend e ⟶ Z),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.extendMap (CategoryTheory.CategoryStruct.comp φ φ') e) h =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.extendMap φ e)
      (CategoryTheory.CategoryStruct.comp (HomologicalComplex.extendMap φ' e) h)

Defined in

Mathlib.Algebra.Homology.Embedding.Extend

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms