Theorems · Theorem · category theory

HomologicalComplex.extend.XOpIso_hom_d_op

∀ {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),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.extend.XOpIso K i).hom (HomologicalComplex.extend.d K j i).op =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.extend.d K.op i j) (HomologicalComplex.extend.XOpIso K j).hom

Defined in: Mathlib.Algebra.Homology.Embedding.Extend
Cited by: 1 results in Mathlib
Foundations: Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.Limits.HasZeroMorphisms

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Cites27

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Oppositestatement and proof · cited by 8,081
CategoryTheory.Iso.homstatement and proof · cited by 7,684
CategoryTheory.Iso.invproof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.Category.id_compproof · cited by 1,998
Quiver.Hom.opstatement and proof · cited by 1,948

Cited by1

Results whose statement or proof uses this declaration.

HomologicalComplex.extend.XOpIso_hom_d_op_assocproof · cited by 0