Theorems · Definition · category theory

CategoryTheory.Limits.ker

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      [CategoryTheory.Limits.HasKernels C] → CategoryTheory.Functor (CategoryTheory.Arrow C) C

The kernel of an arrow is natural.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Kernels
Cited by: 5 results in Mathlib
Foundations: Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasKernels

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

Cites12

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.Homproof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Arrowstatement and proof · cited by 713
CategoryTheory.Arrow.homproof · cited by 335
CategoryTheory.Limits.kernelproof · cited by 272
CategoryTheory.Limits.kernel.ιproof · cited by 214
CategoryTheory.Arrow.Hom.leftproof · cited by 160
CategoryTheory.Limits.HasKernelsstatement and proof · cited by 67
CategoryTheory.Limits.kernel.liftproof · cited by 64

Cited by7

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.ker.ιstatement · cited by 3
CategoryTheory.Limits.ker.conditionstatement · cited by 1
CategoryTheory.Limits.kerIsKernelstatement · cited by 0
CategoryTheory.Limits.ker_mapstatement and proof · cited by 0
CategoryTheory.Limits.ker_objstatement and proof · cited by 0
CategoryTheory.Limits.ker.condition_assocstatement · cited by 0
CategoryTheory.Limits.ker.ι_appstatement · cited by 0