Theorems · Theorem · category theory
CategoryTheory.Preadditive.hasCoequalizer_of_hasCokernel
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] {X Y : C} (f g : X ⟶ Y)
[CategoryTheory.Limits.HasCokernel (f - g)], CategoryTheory.Limits.HasCoequalizer f gA preadditive category has a coequalizer for f and g if it has a cokernel for f - 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
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.HasCokernelstatement and proof · cited by 131
- CategoryTheory.Limits.coequalizer.πproof · cited by 93
- CategoryTheory.Limits.Cofork.ofπproof · cited by 56
- CategoryTheory.Limits.HasCoequalizerstatement · cited by 54
- CategoryTheory.Limits.HasColimit.mkproof · cited by 25
- CategoryTheory.Limits.coequalizer.conditionproof · cited by 16
- CategoryTheory.Preadditive.coforkOfCokernelCoforkproof · cited by 6
- CategoryTheory.Limits.coequalizerIsCoequalizerproof · cited by 5
- CategoryTheory.Preadditive.isColimitCoforkOfCokernelCoforkproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.SerreClassLocalization.hasCoequalizersproof · cited by 0