Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Limits.KernelFork

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

A kernel fork is just a fork 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.KernelFork.ofι · cited by 70KernelFork.ofιCategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelFork · cited by 14LeftHomologyData.ofIsLimi…CategoryTheory.ShortComplex.RightHomologyData.ofIsLimitKernelFork · cited by 13RightHomologyData.ofIsLim…CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.leftHomologyData · cited by 12ofEpiMonoFactorisation.le…CategoryTheory.ShortComplex.isoCyclesOfIsLimit · cited by 11ShortComplex.isoCyclesOfI…CategoryTheory.Limits.KernelFork.IsLimit.lift' · cited by 9IsLimit.lift'CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology · cited by 9ofEpiMonoFactorisation.is…CategoryTheory.ShortComplex.HomologyData.ofIsLimitKernelFork · cited by 8HomologyData.ofIsLimitKer…CategoryTheory.Preadditive.forkOfKernelFork · cited by 8Preadditive.forkOfKernelF…CategoryTheory.Limits.KernelFork.condition · cited by 7KernelFork.conditionCategoryTheory.Limits.KernelFork.isLimitMapConeEquiv · cited by 7KernelFork.isLimitMapCone…CategoryTheory.Preadditive.kernelForkOfFork · cited by 7Preadditive.kernelForkOfF…CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.kf · cited by 6HomologyData.kfCategoryTheory.Limits.KernelFork.map · cited by 6KernelFork.mapCategoryTheory.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.Fork · cited by 85Limits.ForkLimits.KernelForkCITED BYCITES

Cites4

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Cited by180

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