Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_hom_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) (A : Type u')
  [inst_1 : CategoryTheory.Category.{v', u'} A] (x : CategoryTheory.LocallyDiscrete Cᵒᵖ)
  (X : CategoryTheory.Sheaf (J.over (Opposite.unop x.as)) A) (X_1 : (CategoryTheory.Over (Opposite.unop x.as))ᵒᵖ),
  (((J.pseudofunctorOver A).mapId x).hom.toNatTrans.app X).hom.app X_1 =
    X.obj.map ((CategoryTheory.Over.mapId (Opposite.unop x.as)).inv.app (Opposite.unop X_1)).op

Defined in

Mathlib.CategoryTheory.Sites.PseudofunctorSheafOver

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category