Relational Sheaves for a Heyting Algebra

Abstract

We show that for a Heyting algebra $\mathcal{H}$, a relational-presheaf is an idempotent symmetric order-preserving lax-semifunctor. A relational-presheaf is a relational-sheaf, if it is an idempotent infima-preserving lax semifunctor. The associated relational-sheaf functor factors through the category of sheaves for $\mathcal{H}$. Using this and the appropriate comparison theorems we obtain the main result that the associated categories of relational-presheaves and relational-sheaves are each respectively equivalent to the categories of presheaves and sheaves for $\mathcal{H}$.

31 pages

References in corpus (2)

• Categorical structures enriched in a quantaloid: categories, distributors and functors
• Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories