Theorems · Theorem · category theory
CategoryTheory.Abelian.comp_epiDesc
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {X Y : C} (f : X ⟶ Y)
[inst_2 : CategoryTheory.Epi f] {T : C} (g : X ⟶ T)
(hg : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernel.ι f) g = 0),
CategoryTheory.CategoryStruct.comp f (CategoryTheory.Abelian.epiDesc f g hg) = g- Defined in
- Mathlib.CategoryTheory.Abelian.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.Limits.parallelPairproof · cited by 766
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.Limits.kernelstatement · cited by 272
- CategoryTheory.Limits.kernel.ιstatement and proof · cited by 214
- CategoryTheory.Limits.limit.isLimitproof · cited by 146
- CategoryTheory.Limits.limit.coneproof · cited by 97
- CategoryTheory.Limits.IsColimit.facproof · cited by 82
- CategoryTheory.Limits.CokernelCofork.ofπproof · cited by 77
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.comp_epiDesc_assocproof · cited by 0
- CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.fullproof · cited by 0