Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.DescentData.hom_self

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  {F : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete Cᵒᵖ) CategoryTheory.Cat} {ι : Type t} {S : C}
  {X : ι → C} {f : (i : ι) → X i ⟶ S} (self : F.DescentData f) ⦃Y : C⦄ (q : Y ⟶ S) ⦃i : ι⦄ (g : Y ⟶ X i)
  (x : CategoryTheory.CategoryStruct.comp g (f i) = q),
  self.hom q g g ⋯ ⋯ = CategoryTheory.CategoryStruct.id ((F.map g.op.toLoc).toFunctor.obj (self.obj i))

Defined in

Mathlib.CategoryTheory.Sites.Descent.DescentData

Cited by

2 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category