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Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.uliftYoneda

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      [J.Subcanonical] → CategoryTheory.Functor C (CategoryTheory.Sheaf J (Type (max v w)))

Variant of the Yoneda embedding which allows a raise in the universe level for the category of types.

Defined in
Mathlib.CategoryTheory.Sites.Canonical
Cited by
23 results in Mathlib
Foundations
Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.GrothendieckTopology.Subcanonical

Around this declaration

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

CategoryTheory.GrothendieckTopology.uliftYonedaEquiv · cited by 14GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf · cited by 4GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda · cited by 4GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map · cited by 3GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp · cited by 2GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality · cited by 2GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality' · cited by 2GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaIsoYoneda · cited by 2GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply · cited by 1GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv · cited by 0GrothendieckTopology.map_…CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv' · cited by 0GrothendieckTopology.map_…CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_hom_app_app_hom_apply · cited by 0GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaCompSheafToPresheaf_inv_app_app_hom_apply · cited by 0GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply · cited by 0GrothendieckTopology.ulif…CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map · cited by 0GrothendieckTopology.ulif…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.Presheaf.IsSheaf · cited by 991Presheaf.IsSheafCategoryTheory.Sheaf · cited by 763CategoryTheory.SheafCategoryTheory.uliftFunctor · cited by 58CategoryTheory.uliftFunct…CategoryTheory.GrothendieckTopology.Subcanonical · cited by 55GrothendieckTopology.Subc…CategoryTheory.GrothendieckTopology.yoneda · cited by 37GrothendieckTopology.yone…CategoryTheory.sheafCompose · cited by 28CategoryTheory.sheafCompo…GrothendieckTopology.uliftYon…CITED BYCITES

Cites11

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Cited by28

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