Mathlib Map

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 AddGrpCat

If G is an additive group object, then Hom(-, G) is a presheaf of additive groups.

Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Grp
Cited by
9 results in Mathlib
Foundations
Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.AddGrpObj

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.yonedaAddGrp · cited by 7CategoryTheory.yonedaAddG…CategoryTheory.yonedaAddGrpObjIsoOfRepresentableBy · cited by 3CategoryTheory.yonedaAddG…CategoryTheory.yonedaAddGrpObjRepresentableBy · cited by 1CategoryTheory.yonedaAddG…CategoryTheory.yonedaAddGrp_naturality · cited by 1CategoryTheory.yonedaAddG…CategoryTheory.yonedaAddGrpObjIsoOfRepresentableBy_hom · cited by 0CategoryTheory.yonedaAddG…CategoryTheory.yonedaAddGrpObjIsoOfRepresentableBy_inv · cited by 0CategoryTheory.yonedaAddG…CategoryTheory.yonedaAddGrpObj_map · cited by 0CategoryTheory.yonedaAddG…CategoryTheory.yonedaAddGrpObj_obj_coe · cited by 0CategoryTheory.yonedaAddG…CategoryTheory.yonedaAddGrp_map_app · cited by 0CategoryTheory.yonedaAddG…CategoryTheory.yonedaAddGrp_naturality_assoc · cited by 0CategoryTheory.yonedaAddG…CategoryTheory.yonedaAddGrp_obj · cited by 0CategoryTheory.yonedaAddG…CategoryTheory.AddGrpObj.ofRepresentableBy_yonedaAddGrpObjRepresentableBy · cited by 0AddGrpObj.ofRepresentable…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeOpposite.unop · cited by 2231Opposite.unopCategoryTheory.CartesianMonoidalCategory · cited by 947CategoryTheory.CartesianM…CategoryTheory.AddGrpObj · cited by 88CategoryTheory.AddGrpObjAddGrpCat · cited by 80AddGrpCatAddGrpCat.of · cited by 23AddGrpCat.ofAddMonCat.Hom.hom · cited by 21Hom.homAddGrpCat.ofHom · cited by 17AddGrpCat.ofHomCategoryTheory.yonedaAddMonObj · cited by 12CategoryTheory.yonedaAddM…CategoryTheory.yonedaAddGrpObjCITED BYCITES

Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by12

Results whose statement or proof uses this declaration.