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 oil the existing developments by avoiding the assumption of additional axioms for small maps and the use of collection sites.
GAMBINO, N. (2008). The associated sheaf functor theorem in Algebraic Set Theory. ANNALS OF PURE AND APPLIED LOGIC, 156(1), 68-77 [10.1016/j.apal.2008.06.008].
The associated sheaf functor theorem in Algebraic Set Theory
GAMBINO, Nicola
2008-01-01
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 oil the existing developments by avoiding the assumption of additional axioms for small maps and the use of collection sites.
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