Theorems · Inductive type · category theory
CategoryTheory.Limits.HasKernels
(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → [CategoryTheory.Limits.HasZeroMorphisms C] → PropHasKernels represents the existence of kernels for every morphism.
- Cited by
- 67 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Limits.HasZeroMorphismsstatement · cited by 3,275
Cited by106
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.rightHomologyFunctorstatement and proof · cited by 7
- CategoryTheory.ShortComplex.leftHomologyFunctorstatement and proof · cited by 7
- CategoryTheory.Abelian.OfCoimageImageComparisonIsIso.imageMonoFactorisationstatement and proof · cited by 6
- CategoryTheory.ObjectProperty.SerreClassLocalization.abelianproof · cited by 6
- imageToKernel'statement and proof · cited by 6
- CategoryTheory.ShortComplex.opcyclesFunctorstatement and proof · cited by 5
- ModuleCat.hasKernels_moduleCatstatement · cited by 5
- CategoryTheory.Limits.kerstatement and proof · cited by 5
- CategoryTheory.ShortComplex.cyclesFunctorstatement and proof · cited by 5
- CategoryTheory.Functor.preservesFiniteLimits_of_preservesHomologystatement and proof · cited by 4
- CategoryTheory.isIso_iff_nonzerostatement and proof · cited by 3
- CategoryTheory.Limits.ker.ιstatement and proof · cited by 3