Theorems · Theorem · category theory

CategoryTheory.OverPresheafAux.yonedaCollectionPresheafToA_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A : CategoryTheory.Functor Cᵒᵖ (Type v)}
  (F : CategoryTheory.Functor (CategoryTheory.CostructuredArrow CategoryTheory.yoneda A)ᵒᵖ (Type v)) (x : Cᵒᵖ),
  (CategoryTheory.OverPresheafAux.yonedaCollectionPresheafToA F).app x =
    TypeCat.ofHom CategoryTheory.OverPresheafAux.YonedaCollection.yonedaEquivFst

Defined in: Mathlib.CategoryTheory.Comma.Presheaf.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites13

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.Homstatement · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
Oppositestatement and proof · cited by 8,081
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
Opposite.unopstatement · cited by 2,231
CategoryTheory.CostructuredArrowstatement and proof · cited by 536
TypeCat.ofHomstatement · cited by 389
CategoryTheory.yonedastatement and proof · cited by 351
CategoryTheory.OverPresheafAux.yonedaCollectionPresheafstatement · cited by 21
CategoryTheory.OverPresheafAux.yonedaCollectionPresheafToAstatement and proof · cited by 13

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.OverPresheafAux.OverArrows.yonedaCollectionPresheafToA_val_fstproof · cited by 4