Theorems · Definition · category theory
CategoryTheory.yonedaAddGrpObj
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
(G : C) → [CategoryTheory.AddGrpObj G] → CategoryTheory.Functor Cᵒᵖ AddGrpCatIf G is an additive group object, then Hom(-, G) is a presheaf of additive groups.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- Opposite.unopproof · cited by 2,231
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.AddGrpObjstatement and proof · cited by 88
- AddGrpCatstatement · cited by 80
- AddGrpCat.ofproof · cited by 23
- AddMonCat.Hom.homproof · cited by 21
- AddGrpCat.ofHomproof · cited by 17
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.yonedaAddGrpproof · cited by 7
- CategoryTheory.yonedaAddGrpObjIsoOfRepresentableBystatement and proof · cited by 3
- CategoryTheory.yonedaAddGrpObjRepresentableBystatement · cited by 1
- CategoryTheory.yonedaAddGrp_naturalitystatement and proof · cited by 1
- CategoryTheory.yonedaAddGrpObjIsoOfRepresentableBy_homstatement · cited by 0
- CategoryTheory.yonedaAddGrpObjIsoOfRepresentableBy_invstatement · cited by 0
- CategoryTheory.yonedaAddGrpObj_mapstatement and proof · cited by 0
- CategoryTheory.yonedaAddGrpObj_obj_coestatement and proof · cited by 0
- CategoryTheory.yonedaAddGrp_map_appstatement · cited by 0
- CategoryTheory.yonedaAddGrp_naturality_assocstatement and proof · cited by 0
- CategoryTheory.yonedaAddGrp_objstatement · cited by 0
- CategoryTheory.AddGrpObj.ofRepresentableBy_yonedaAddGrpObjRepresentableBystatement and proof · cited by 0