Theorems · Definition · category theory

CategoryTheory.InjectiveResolution.Hom.hom

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] →
      [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
        {Z : C} →
          {I : CategoryTheory.InjectiveResolution Z} →
            {Z' : C} →
              {I' : CategoryTheory.InjectiveResolution Z'} → {f : Z ⟶ Z'} → I.Hom I' f → (I.cocomplex ⟶ I'.cocomplex)

A morphism between the cocomplexes

Defined in: Mathlib.CategoryTheory.Preadditive.Injective.Resolution
Cited by: 8 results in Mathlib
Foundations: Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.Limits.HasZeroMorphisms

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Around this declaration

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

Cites9

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
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement · cited by 1,016
CategoryTheory.InjectiveResolutionstatement and proof · cited by 90
CategoryTheory.InjectiveResolution.cocomplexstatement · cited by 73
CategoryTheory.InjectiveResolution.Homstatement and proof · cited by 12

Cited by9

Results whose statement or proof uses this declaration.

CategoryTheory.InjectiveResolution.Hom.hom'proof · cited by 5
CategoryTheory.InjectiveResolution.Hom.hom'_fstatement and proof · cited by 3
CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom'proof · cited by 2
CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zerostatement · cited by 2
CategoryTheory.InjectiveResolution.Hom.ι_comp_homstatement · cited by 1
CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zero_assocstatement and proof · cited by 1
CategoryTheory.InjectiveResolution.Hom.hom'_f_assocstatement and proof · cited by 0
CategoryTheory.InjectiveResolution.extMk_comp_mk₀statement and proof · cited by 0
CategoryTheory.InjectiveResolution.Hom.ι_comp_hom_assocstatement and proof · cited by 0