Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.pseudofunctorOver_mapComp_inv_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] {a b c : CategoryTheory.LocallyDiscrete Cᵒᵖ} (x : a ⟶ b) (x_1 : b ⟶ c)
  (X : CategoryTheory.Sheaf (J.over (Opposite.unop a.as)) A) (X_1 : (CategoryTheory.Over (Opposite.unop c.as))ᵒᵖ),
  (((J.pseudofunctorOver A).mapComp x x_1).inv.toNatTrans.app X).hom.app X_1 =
    X.obj.map ((CategoryTheory.Over.mapComp x_1.as.unop x.as.unop).hom.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