Mathlib Map

Theorems · Definition · category theory

CategoryTheory.yonedaGrp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      CategoryTheory.Functor (CategoryTheory.Grp C) (CategoryTheory.Functor Cᵒᵖ GrpCat)

The yoneda embedding of Grp C into presheaves of groups.

Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Grp
Cited by
9 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory

Around this declaration

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

CategoryTheory.GrpObj.comp_inv · cited by 10GrpObj.comp_invCategoryTheory.shrinkYonedaGrp · cited by 5CategoryTheory.shrinkYone…CategoryTheory.GrpObj.comp_div · cited by 1GrpObj.comp_divCategoryTheory.GrpObj.div_comp · cited by 1GrpObj.div_compCategoryTheory.GrpObj.zpow_comp · cited by 1GrpObj.zpow_compCategoryTheory.yonedaGrp_map_app · cited by 0CategoryTheory.yonedaGrp_…CategoryTheory.yonedaGrp_obj · cited by 0CategoryTheory.yonedaGrp_…CategoryTheory.shrinkYonedaGrp_map · cited by 0CategoryTheory.shrinkYone…CategoryTheory.shrinkYonedaGrp_obj · cited by 0CategoryTheory.shrinkYone…CategoryTheory.yonedaGrpFullyFaithful · cited by 0CategoryTheory.yonedaGrpF…CategoryTheory.essImage_yonedaGrp · cited by 0CategoryTheory.essImage_y…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.CartesianMonoidalCategory · cited by 947CategoryTheory.CartesianM…CategoryTheory.InducedCategory.Hom.hom · cited by 850Hom.homGrpCat · cited by 146GrpCatCategoryTheory.Grp · cited by 144CategoryTheory.GrpCategoryTheory.Grp.X · cited by 99Grp.XMonCat.Hom.hom · cited by 38Hom.homGrpCat.ofHom · cited by 23GrpCat.ofHomCategoryTheory.yonedaMon · cited by 10CategoryTheory.yonedaMonCategoryTheory.yonedaGrpObj · cited by 9CategoryTheory.yonedaGrpO…CategoryTheory.yonedaGrpCITED BYCITES

Cites15

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

Cited by11

Results whose statement or proof uses this declaration.