Theorems · Theorem · category theory
CategoryTheory.Preadditive.hasWeakKernel_of_hasWeakEqualizer
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] {X Y : C}
(f g : X ⟶ Y) [CategoryTheory.Limits.HasWeakEqualizer f g], CategoryTheory.Limits.HasWeakKernel (f - g)A preadditive category has a weak kernel for f - g if it has a weak equalizer
for f and g.
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- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
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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.HasWeakEqualizerstatement and proof · cited by 10
- CategoryTheory.Limits.HasWeakKernelstatement · cited by 8
- CategoryTheory.Preadditive.kernelForkOfForkproof · cited by 7
- CategoryTheory.Limits.HasWeakLimit.mkproof · cited by 4
- CategoryTheory.Limits.weakLimit.isWeakLimitproof · cited by 4
- CategoryTheory.Limits.weakEqualizer.forkproof · cited by 3
- CategoryTheory.Preadditive.isWeakLimitKernelForkOfForkproof · cited by 1
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