Theorems · Definition · category theory

CategoryTheory.linearYoneda

(R : Type w) →
  [inst : Ring R] →
    (C : Type u) →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        [inst_2 : CategoryTheory.Preadditive C] →
          [CategoryTheory.Linear R C] → CategoryTheory.Functor C (CategoryTheory.Functor Cᵒᵖ (ModuleCat R))

The Yoneda embedding for R-linear categories C sending an object X : C to the ModuleCat R-valued presheaf on C, with value on Y : Cᵒᵖ given by ModuleCat.of R (unop Y ⟶ X).

Defined in

Mathlib.CategoryTheory.Linear.Yoneda

Cited by

7 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Linear