Theorems · Theorem · category theory

TopCat.Presheaf.IsSheaf.isSheafPairwiseIntersections

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X : TopCat} {F : TopCat.Presheaf C X} {ι : Type u_2}
  (U : ι → TopologicalSpace.Opens ↑X),
  F.IsSheaf →
    Nonempty (CategoryTheory.Limits.IsLimit (CategoryTheory.Functor.mapCone F (CategoryTheory.Pairwise.cocone U).op))

Defined in

Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category