Theorems · Definition · category theory

HomologicalComplex.extend.d

{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) → HomologicalComplex.extend.X K i ⟶ HomologicalComplex.extend.X K j

Auxiliary definition for the d field of HomologicalComplex.extend.

Defined in: Mathlib.Algebra.Homology.Embedding.Extend
Cited by: 5 results in Mathlib
Foundations: Depth 11 from the axioms · uses Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.Limits.HasZeroMorphisms

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

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 and proof · cited by 32,603
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
HomologicalComplexstatement and proof · cited by 1,691
ComplexShapestatement and proof · cited by 1,684
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
HomologicalComplex.dproof · cited by 598
HomologicalComplex.extend.Xstatement and proof · cited by 13

Cited by6

Results whose statement or proof uses this declaration.

HomologicalComplex.extendproof · cited by 115
HomologicalComplex.extend.d_eqstatement · cited by 2
HomologicalComplex.extend.d_none_eq_zerostatement and proof · cited by 2
HomologicalComplex.extend.d_none_eq_zero'statement and proof · cited by 2
HomologicalComplex.extend.XOpIso_hom_d_opstatement and proof · cited by 1
HomologicalComplex.extend.XOpIso_hom_d_op_assocstatement and proof · cited by 0