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Theorems · Definition · category theory

CategoryTheory.Limits.CokernelCofork

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.Limits.HasZeroMorphisms C] → {X Y : C} → (X ⟶ Y) → Type (max u v)

A cokernel cofork is just a cofork where the second morphism is a zero morphism.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Kernels
Cited by
108 results in Mathlib
Foundations
Depth 20 from the axioms, rests on 87 definitions · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

CategoryTheory.Limits.CokernelCofork.ofπ · cited by 77CokernelCofork.ofπCategoryTheory.ShortComplex.LeftHomologyData.ofIsColimitCokernelCofork · cited by 13LeftHomologyData.ofIsColi…CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.leftHomologyData · cited by 12ofEpiMonoFactorisation.le…CategoryTheory.ShortComplex.isoOpcyclesOfIsColimit · cited by 12ShortComplex.isoOpcyclesO…CategoryTheory.ShortComplex.RightHomologyData.ofIsColimitCokernelCofork · cited by 12RightHomologyData.ofIsCol…CategoryTheory.Limits.CokernelCofork.condition · cited by 10CokernelCofork.conditionCategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology · cited by 9ofEpiMonoFactorisation.is…CategoryTheory.Limits.CokernelCofork.IsColimit.desc' · cited by 8IsColimit.desc'CategoryTheory.Limits.CokernelCofork.isColimitMapCoconeEquiv · cited by 7CokernelCofork.isColimitM…CategoryTheory.Limits.CokernelCofork.map · cited by 7CokernelCofork.mapCategoryTheory.Limits.CokernelCofork.mapIsColimit · cited by 7CokernelCofork.mapIsColim…CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.cc · cited by 6HomologyData.ccCategoryTheory.ShortComplex.HomologyData.ofIsColimitCokernelCofork · cited by 6HomologyData.ofIsColimitC…CategoryTheory.Preadditive.coforkOfCokernelCofork · cited by 6Preadditive.coforkOfCoker…CategoryTheory.ComposableArrows.Exact.cokerIsoKer' · cited by 6Exact.cokerIsoKer'CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.Cofork · cited by 80Limits.CoforkLimits.CokernelCoforkCITED BYCITES

Cites4

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Cited by188

Results whose statement or proof uses this declaration.