Theorems · Theorem · category theory

HomologicalComplex.extend_op_d_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 : HomologicalComplex C c) (e : c.Embedding c') (i' j' : ι')
  {Z : Cᵒᵖ} (h : (K.op.extend e.op).X j' ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((K.op.extend e.op).d i' j') h =
    CategoryTheory.CategoryStruct.comp ((K.extendOpIso e).hom.f i')
      (CategoryTheory.CategoryStruct.comp ((K.extend e).d j' i').op
        (CategoryTheory.CategoryStruct.comp ((K.extendOpIso e).inv.f j') h))

Defined in

Mathlib.Algebra.Homology.Embedding.Extend

Cited by

0 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms