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Theorems · Definition · category theory

CategoryTheory.yonedaMon

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v, u_1} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      CategoryTheory.Functor (CategoryTheory.Mon C) (CategoryTheory.Functor Cᵒᵖ MonCat)

The yoneda embedding of Mon C into presheaves of monoids.

Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Mon
Cited by
10 results in Mathlib
Foundations
Depth 43 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.MonObj.comp_mul · cited by 10MonObj.comp_mulCategoryTheory.yonedaGrp · cited by 9CategoryTheory.yonedaGrpCategoryTheory.MonObj.comp_one · cited by 7MonObj.comp_oneCategoryTheory.shrinkYonedaMon · cited by 5CategoryTheory.shrinkYone…CategoryTheory.Hom.mulEquivCongrRight · cited by 2Hom.mulEquivCongrRightCategoryTheory.yonedaGrp_map_app · cited by 0CategoryTheory.yonedaGrp_…CategoryTheory.yonedaMonFullyFaithful · cited by 0CategoryTheory.yonedaMonF…CategoryTheory.yonedaMon_map_app · cited by 0CategoryTheory.yonedaMon_…CategoryTheory.shrinkYonedaMon_map · cited by 0CategoryTheory.shrinkYone…CategoryTheory.yonedaMon_obj · cited by 0CategoryTheory.yonedaMon_…CategoryTheory.shrinkYonedaMon_obj · cited by 0CategoryTheory.shrinkYone…CategoryTheory.essImage_yonedaMon · cited by 0CategoryTheory.essImage_y…CategoryTheory.Hom.mulEquivCongrRight_apply · cited by 0Hom.mulEquivCongrRight_ap…CategoryTheory.Hom.mulEquivCongrRight_symm_apply · cited by 0Hom.mulEquivCongrRight_sy…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeOpposite.unop · cited by 2231Opposite.unopCategoryTheory.CartesianMonoidalCategory · cited by 947CategoryTheory.CartesianM…CategoryTheory.Mon · cited by 465CategoryTheory.MonCategoryTheory.Mon.X · cited by 329Mon.XCategoryTheory.Mon.Hom.hom · cited by 200Hom.homMonCat · cited by 127MonCatMonCat.ofHom · cited by 24MonCat.ofHomCategoryTheory.yonedaMonObj · cited by 12CategoryTheory.yonedaMonO…CategoryTheory.IsMonHom.monoidHom · cited by 10IsMonHom.monoidHomCategoryTheory.yonedaMonCITED BYCITES

Cites13

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

Cited by14

Results whose statement or proof uses this declaration.