Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.isStackFor_ofArrows_iff

∀ {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),
  F.IsStackFor (CategoryTheory.Presieve.ofArrows X f) ↔ (F.toDescentData f).IsEquivalence

Defined in

Mathlib.CategoryTheory.Sites.Descent.DescentData

Cited by

2 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category