Theorems · Theorem · category theory
CategoryTheory.Abelian.OfCoimageImageComparisonIsIso.imageMonoFactorisation_e
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.Limits.HasKernels C] [inst_3 : CategoryTheory.Limits.HasCokernels C] {X Y : C} (f : X ⟶ Y),
(CategoryTheory.Abelian.OfCoimageImageComparisonIsIso.imageMonoFactorisation f).e =
CategoryTheory.Limits.kernel.lift (CategoryTheory.Limits.cokernel.π f) f ⋯- Defined in
- Mathlib.CategoryTheory.Abelian.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 36 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.kernelstatement · cited by 272
- CategoryTheory.Limits.cokernelstatement · cited by 229
- CategoryTheory.Limits.cokernel.πstatement · cited by 194
- CategoryTheory.Limits.HasKernelsstatement and proof · cited by 67
- CategoryTheory.Limits.kernel.liftstatement · cited by 64
- CategoryTheory.Limits.HasCokernelsstatement and proof · cited by 47
- CategoryTheory.Limits.MonoFactorisation.estatement and proof · cited by 39
- CategoryTheory.Abelian.OfCoimageImageComparisonIsIso.imageMonoFactorisationstatement and proof · cited by 6
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