Theorems · Definition · category theory
CategoryTheory.Abelian.Preradical
(C : Type u) → [CategoryTheory.Category.{v, u} C] → Type (max u v)A preradical on an abelian category C is a monomorphism in C ⥤ C with codomain 𝟭 C.
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.MonoOverproof · cited by 115
Cited by49
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Preradical.rstatement and proof · cited by 23
- CategoryTheory.Abelian.Preradical.quotientstatement and proof · cited by 20
- CategoryTheory.Abelian.Preradical.ιstatement and proof · cited by 15
- CategoryTheory.Abelian.Preradical.colonstatement and proof · cited by 13
- CategoryTheory.Abelian.Preradical.πstatement and proof · cited by 10
- CategoryTheory.Abelian.Preradical.colonπstatement and proof · cited by 9
- CategoryTheory.Abelian.Preradical.toColonstatement and proof · cited by 9
- CategoryTheory.Abelian.Preradical.shortComplexstatement and proof · cited by 6
- CategoryTheory.Abelian.Preradical.shortComplexObjstatement and proof · cited by 6
- CategoryTheory.Abelian.Preradical.isRadicalstatement and proof · cited by 3
- CategoryTheory.Abelian.Preradical.colon_ι_app_π_appstatement and proof · cited by 2
- CategoryTheory.Abelian.Preradical.isPullback_colonstatement and proof · cited by 2