Theorems · Definition · category theory

CategoryTheory.InjectiveResolution.self

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] →
      [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
        (Z : C) → [CategoryTheory.Injective Z] → CategoryTheory.InjectiveResolution Z

An injective object admits a trivial injective resolution: itself in degree 0.

Defined in: Mathlib.CategoryTheory.Preadditive.Injective.Resolution
Cited by: 3 results in Mathlib
Foundations: Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Injective

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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
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.InjectiveResolutionstatement · cited by 90
CategoryTheory.Injectivestatement and proof · cited by 70
CochainComplex.single₀proof · cited by 59

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.isZero_rightDerived_obj_injective_succproof · cited by 0
CategoryTheory.InjectiveResolution.self_cocomplexstatement and proof · cited by 0
CategoryTheory.InjectiveResolution.self_ιstatement and proof · cited by 0