Theorems · Definition · category theory

CategoryTheory.ProjectiveResolution.isColimitCokernelCofork

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroObject C] →
      [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
        {Z : C} → (P : CategoryTheory.ProjectiveResolution Z) → CategoryTheory.Limits.IsColimit P.cokernelCofork

Z is the cokernel of P.complex.X 1 ⟶ P.complex.X 0 when P : ProjectiveResolution Z.

Defined in: Mathlib.CategoryTheory.Preadditive.Projective.Resolution
Cited by: 1 results in Mathlib
Foundations: Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.Limits.HasZeroMorphisms

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites22

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.Iso.symmproof · cited by 993
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.IsColimitstatement · cited by 773
CategoryTheory.Limits.parallelPairstatement · cited by 766
ComplexShape.downstatement and proof · cited by 605
HomologicalComplex.dstatement · cited by 598
CategoryTheory.Iso.transproof · cited by 566

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.ProjectiveResolution.exact₀proof · cited by 2