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Theorems · Definition · category theory

CategoryTheory.Preadditive.forkOfKernelFork

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {X Y : C} → {f g : X ⟶ Y} → CategoryTheory.Limits.KernelFork (f - g) → CategoryTheory.Limits.Fork f g

Map a kernel cone on the difference of two morphisms to the equalizer fork.

Defined in
Mathlib.CategoryTheory.Preadditive.Basic
Cited by
8 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Preadditive
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel · cited by 5Limits.binaryBiconeOfIsSp…CategoryTheory.Preadditive.isLimitForkOfKernelFork · cited by 4Preadditive.isLimitForkOf…CategoryTheory.Preadditive.hasEqualizer_of_hasKernel · cited by 2Preadditive.hasEqualizer_…CategoryTheory.Preadditive.isLimitKernelForkOfFork · cited by 2Preadditive.isLimitKernel…CategoryTheory.Preadditive.isWeakLimitForkOfKernelFork · cited by 2Preadditive.isWeakLimitFo…CategoryTheory.Preadditive.hasWeakEqualizer_of_hasWeakKernel · cited by 1Preadditive.hasWeakEquali…CategoryTheory.Functor.preservesEqualizer_of_preservesKernels · cited by 1Functor.preservesEqualize…CategoryTheory.Preadditive.isWeakLimitKernelForkOfFork · cited by 1Preadditive.isWeakLimitKe…CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_fst · cited by 0Limits.binaryBiconeOfIsSp…CategoryTheory.Preadditive.forkOfKernelFork_pt · cited by 0Preadditive.forkOfKernelF…CategoryTheory.Preadditive.forkOfKernelFork_ι · cited by 0Preadditive.forkOfKernelF…CategoryTheory.Preadditive.isLimitForkOfKernelFork_lift · cited by 0Preadditive.isLimitForkOf…CategoryTheory.Preadditive.isWeakLimitForkOfKernelFork_lift · cited by 0Preadditive.isWeakLimitFo…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.Limits.Fork.ι · cited by 162Fork.ιCategoryTheory.Limits.KernelFork · cited by 108Limits.KernelForkCategoryTheory.Limits.Fork · cited by 85Limits.ForkCategoryTheory.Limits.Fork.ofι · cited by 66Fork.ofιPreadditive.forkOfKernelForkCITED BYCITES

Cites7

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Cited by13

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