Theorems · Definition · category theory

CategoryTheory.InjectiveResolution.isLimitKernelFork

{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) → CategoryTheory.Limits.IsLimit I.kernelFork

Z is the kernel of I.cocomplex.X 0 ⟶ I.cocomplex.X 1 when I : InjectiveResolution Z.

Defined in: Mathlib.CategoryTheory.Preadditive.Injective.Resolution
Cited by: 1 results in Mathlib
Foundations: Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.Limits.HasZeroMorphisms

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Cites23

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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
HomologicalComplex.Xstatement · cited by 1,839
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.Limits.Cone.ptproof · cited by 1,298
ComplexShape.upstatement and proof · cited by 1,123
CategoryTheory.Iso.symmproof · cited by 993
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.parallelPairstatement · cited by 766
CategoryTheory.Limits.IsLimitstatement · cited by 664
HomologicalComplex.dstatement · cited by 598

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.InjectiveResolution.exact₀proof · cited by 2