Theorems · Theorem · category theory
CategoryTheory.Abelian.comp_epiDesc_assoc
∀ {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) {Z : C} (h : T ⟶ Z),
CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp (CategoryTheory.Abelian.epiDesc f g hg) h) =
CategoryTheory.CategoryStruct.comp g h- Defined in
- Mathlib.CategoryTheory.Abelian.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.Limits.kernelstatement · cited by 272
- CategoryTheory.Limits.kernel.ιstatement and proof · cited by 214
- CategoryTheory.Abelian.nonPreadditiveAbelianstatement · cited by 16
- CategoryTheory.Abelian.epiDescstatement and proof · cited by 5
- CategoryTheory.Abelian.comp_epiDescproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.