The associated sheaf functor theorem in algebraic set theory

Abstract. We prove a version of the associated sheaf functor theorem in Algebraic Set Theory. The proof is established working within a Heyting pretopos equipped with a system of small maps satisfying the axioms originally introduced by Joyal and Moerdijk. This result improves on the existing developments by avoiding the assumption of additional axioms for small maps and the use of collection sites.

• Type: Journal
• Year: 2008
• Where: APAL
• Authors: Nicola Gambino
• Keywords: Algebraic Set Theory, APAL 2008, Sheaf Functor Theorem, Small Maps