Theorems · Definition · category theory

CategoryTheory.yonedaCommRing

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] →
        CategoryTheory.Functor (CategoryTheory.CommRingObjCat C) (CategoryTheory.Functor Cᵒᵖ CommRingCat)

The yoneda embedding of CommRingObjCat C into presheaves of commutative rings.

Defined in: Mathlib.CategoryTheory.Monoidal.Cartesian.Ring
Cited by: 2 results in Mathlib
Foundations: Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory CategoryTheory.BraidedCategory

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Around this declaration

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

Cites14

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
CommRingCatstatement · cited by 2,333
Opposite.unopproof · cited by 2,231
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
CategoryTheory.BraidedCategorystatement and proof · cited by 779
CommRingCat.ofHomproof · cited by 259
CategoryTheory.CommRingObjCatstatement and proof · cited by 19
CategoryTheory.CommRingObjCat.Xproof · cited by 16

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.yonedaCommRing_objstatement and proof · cited by 0
CategoryTheory.yonedaCommRing_map_app_applystatement · cited by 0