Theorems · Definition · category theory
CategoryTheory.preadditiveCoyonedaObj
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Preadditive C] → (X : C) → CategoryTheory.Functor C (ModuleCat (CategoryTheory.End X)ᵐᵒᵖ)The Yoneda embedding for preadditive categories sends an object X to the copresheaf sending an
object Y to the End X-module of morphisms X ⟶ Y.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, 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.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- ModuleCatstatement · cited by 1,429
- MulOppositestatement and proof · cited by 1,135
- ModuleCat.ofproof · cited by 594
- ModuleCat.ofHomproof · cited by 200
- CategoryTheory.Endstatement and proof · cited by 169
- CategoryTheory.Preadditive.add_compproof · cited by 82
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.preadditiveCoyonedaproof · cited by 10
- CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesInjectiveObjectsstatement and proof · cited by 1
- CategoryTheory.preadditiveCoyonedaObj_mapstatement and proof · cited by 1
- CategoryTheory.preadditiveCoyoneda_objstatement · cited by 1
- CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyonedaObjstatement and proof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.tensorObjproof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.tensorObjPreadditiveCoyonedaObjAdjunctionstatement and proof · cited by 1
- CategoryTheory.Abelian.preadditiveCoyonedaObj_map_surjectivestatement and proof · cited by 1
- CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObjstatement and proof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.fullstatement and proof · cited by 0
- CategoryTheory.preadditiveCoyonedaObj_obj_carrierstatement and proof · cited by 0