Theorems · Definition · category theory

CategoryTheory.shrinkCoyonedaCorepresentableBy

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] →
      (X : Cᵒᵖ) → (CategoryTheory.shrinkCoyoneda.{w, v, u}.obj X).CorepresentableBy (Opposite.unop X)

shrinkCoyoneda.obj X is corepresented by X.

Defined in: Mathlib.CategoryTheory.ShrinkYoneda
Cited by: 2 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.LocallySmall

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

Cites10

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
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement · cited by 16,252
Oppositestatement and proof · cited by 8,081
Equiv.symmproof · cited by 3,681
Opposite.unopstatement · cited by 2,231
CategoryTheory.LocallySmallstatement and proof · cited by 242
CategoryTheory.Functor.CorepresentableBystatement · cited by 27
CategoryTheory.shrinkCoyonedastatement · cited by 23
CategoryTheory.shrinkCoyonedaObjObjEquivproof · cited by 17

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.GrothendieckTopology.IsLocalSite.pointPresheafFiberIsoproof · cited by 4
CategoryTheory.GrothendieckTopology.IsLocalSite.toPresheafFiber_pointPresheafFiberIso_homproof · cited by 2
CategoryTheory.shrinkCoyonedaCorepresentableBy_homEquivstatement and proof · cited by 0