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.
- Cited by
- 108 results in Mathlib
- Foundations
- Depth 20 from the axioms, rests on 87 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Forkproof · cited by 85
Cited by180
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.KernelFork.ofιstatement · cited by 70
- CategoryTheory.ShortComplex.LeftHomologyData.ofIsLimitKernelForkstatement and proof · cited by 14
- CategoryTheory.ShortComplex.RightHomologyData.ofIsLimitKernelForkstatement and proof · cited by 13
- CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.leftHomologyDatastatement and proof · cited by 12
- CategoryTheory.ShortComplex.isoCyclesOfIsLimitstatement and proof · cited by 11
- CategoryTheory.Limits.KernelFork.IsLimit.lift'statement and proof · cited by 9
- CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomologystatement and proof · cited by 9
- CategoryTheory.ShortComplex.HomologyData.ofIsLimitKernelForkstatement and proof · cited by 8
- CategoryTheory.Preadditive.forkOfKernelForkstatement and proof · cited by 8
- CategoryTheory.Limits.KernelFork.conditionstatement and proof · cited by 7
- CategoryTheory.Limits.KernelFork.isLimitMapConeEquivstatement and proof · cited by 7
- CategoryTheory.Preadditive.kernelForkOfForkstatement · cited by 7