Theorems · Theorem · category theory

TopCat.Presheaf.isSheafOpensLeCover_iff_isSheafPairwiseIntersections

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X : TopCat} (F : TopCat.Presheaf C X),
  F.IsSheafOpensLeCover ↔ F.IsSheafPairwiseIntersections

The sheaf condition in terms of a limit diagram over all { V : Opens X // ∃ i, V ≤ U i } is equivalent to the reformulation in terms of a limit diagram over U i and U i ⊓ U j.

Defined in

Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category