Theorems · Theorem · category theory
CategoryTheory.Preadditive.hasKernel_of_hasEqualizer
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] {X Y : C} (f g : X ⟶ Y)
[CategoryTheory.Limits.HasEqualizer f g], CategoryTheory.Limits.HasKernel (f - g)A preadditive category has a kernel for f - g if it has an equalizer for f and g.
- Defined in
- Mathlib.CategoryTheory.Preadditive.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
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.parallelPairproof · cited by 766
- CategoryTheory.Limits.HasKernelstatement · cited by 169
- CategoryTheory.Limits.limit.isLimitproof · cited by 146
- CategoryTheory.Limits.HasEqualizerstatement and proof · cited by 47
- CategoryTheory.Limits.HasLimit.mkproof · cited by 29
- CategoryTheory.Preadditive.kernelForkOfForkproof · cited by 7
- CategoryTheory.Limits.equalizer.forkproof · cited by 3
- CategoryTheory.Preadditive.isLimitKernelForkOfForkproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.