Theorems · Definition · category theory

CategoryTheory.yonedaCommGrpGrpObj

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] →
        CategoryTheory.CommGrp C → CategoryTheory.Functor (CategoryTheory.Grp C)ᵒᵖ CommGrpCat

The yoneda embedding of CommGrp C into presheaves of groups.

Defined in: Mathlib.CategoryTheory.Monoidal.Cartesian.CommGrp_
Cited by: 4 results in Mathlib
Foundations: Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory CategoryTheory.BraidedCategory

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

Cites15

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
Oppositestatement and proof · cited by 8,081
Opposite.unopproof · cited by 2,231
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
Quiver.Hom.unopproof · cited by 903
CategoryTheory.BraidedCategorystatement and proof · cited by 779
CategoryTheory.Grpstatement and proof · cited by 144
CategoryTheory.CommGrpstatement and proof · cited by 74
CommGrpCatstatement · cited by 74

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.yonedaCommGrpGrpproof · cited by 2
CategoryTheory.yonedaCommGrpGrpObj_obj_coestatement and proof · cited by 0
CategoryTheory.yonedaCommGrpGrp_map_appstatement · cited by 0
CategoryTheory.yonedaCommGrpGrp_objstatement · cited by 0
CategoryTheory.yonedaCommGrpGrpObj_mapstatement and proof · cited by 0