Theorems · Definition · category theory
CategoryTheory.Preadditive.kernelForkOfFork
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Preadditive C] →
{X Y : C} → {f g : X ⟶ Y} → CategoryTheory.Limits.Fork f g → CategoryTheory.Limits.KernelFork (f - g)Map any equalizer fork to a cone on the difference of the two morphisms.
- Defined in
- Mathlib.CategoryTheory.Preadditive.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.Limits.Fork.ιproof · cited by 162
- CategoryTheory.Limits.KernelForkstatement · cited by 108
- CategoryTheory.Limits.Forkstatement and proof · cited by 85
- CategoryTheory.Limits.Fork.ofιproof · cited by 66
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.Preadditive.isLimitForkOfKernelForkproof · cited by 4
- CategoryTheory.Preadditive.isLimitKernelForkOfForkstatement and proof · cited by 2
- CategoryTheory.Preadditive.isWeakLimitForkOfKernelForkproof · cited by 2
- CategoryTheory.Preadditive.isWeakLimitKernelForkOfForkstatement and proof · cited by 1
- CategoryTheory.Preadditive.hasKernel_of_hasEqualizerproof · cited by 1
- CategoryTheory.Functor.preservesEqualizer_of_preservesKernelsproof · cited by 1
- CategoryTheory.Preadditive.isLimitForkOfKernelFork_liftstatement · cited by 0
- CategoryTheory.Preadditive.isWeakLimitForkOfKernelFork_liftstatement · cited by 0
- CategoryTheory.Preadditive.kernelForkOfFork_ofιstatement · cited by 0
- CategoryTheory.Preadditive.kernelForkOfFork_ιstatement · cited by 0
- CategoryTheory.Preadditive.hasWeakKernel_of_hasWeakEqualizerproof · cited by 0