Lawvere-Tierney sheaves in algebraic set theory
Logic
2014-11-21 v3 Category Theory
Abstract
We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.
Keywords
Cite
@article{arxiv.0711.1529,
title = {Lawvere-Tierney sheaves in algebraic set theory},
author = {Steve Awodey and Nicola Gambino and Peter L. Lumsdaine and Michael A. Warren},
journal= {arXiv preprint arXiv:0711.1529},
year = {2014}
}
Comments
33 pages; a revised version of the earlier paper "A general construction of internal sheaves in algebraic set theory"; accepted for publication in the Journal of Symbolic Logic