Theorems · Definition · category theory
CategoryTheory.Limits.HasKernel
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → [CategoryTheory.Limits.HasZeroMorphisms C] → {X Y : C} → (X ⟶ Y) → PropA morphism f has a kernel if the functor ParallelPair f 0 has a limit.
- Cited by
- 169 results in Mathlib
- Foundations
- Depth 19 from the axioms, rests on 86 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 32,603
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Limits.parallelPairproof · cited by 766
- CategoryTheory.Limits.HasLimitproof · cited by 226
Cited by222
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.kernelstatement and proof · cited by 272
- CategoryTheory.Limits.kernel.ιstatement and proof · cited by 214
- CategoryTheory.Limits.kernel.liftstatement and proof · cited by 64
- CategoryTheory.Limits.kernelSubobjectstatement and proof · cited by 58
- CategoryTheory.Abelian.imagestatement and proof · cited by 57
- CategoryTheory.Limits.kernel.lift_ιstatement and proof · cited by 55
- CategoryTheory.Limits.kernel.conditionstatement and proof · cited by 52
- CategoryTheory.Abelian.coimagestatement and proof · cited by 44
- CategoryTheory.Limits.kernel.mapstatement and proof · cited by 32
- CategoryTheory.Abelian.image.ιstatement and proof · cited by 25
- CategoryTheory.Limits.kernelIsKernelstatement and proof · cited by 24
- imageToKernelstatement and proof · cited by 21
Showing the 200 most cited of 222.