Factorizing the Top-Loc adjunction through positive topologies
General Topology
2018-12-24 v1 Logic in Computer Science
Category Theory
Logic
Abstract
We characterize the category of Sambin's positive topologies as a fibration over the category of locales Loc. The fibration is obtained by applying the Grothendieck construction to a doctrine over Loc. We then construct an adjunction between the category of positive topologies and that of topological spaces Top, and show that the well-known adjunction between Top and Loc factors through the newly constructed adjunction.
Cite
@article{arxiv.1812.09190,
title = {Factorizing the Top-Loc adjunction through positive topologies},
author = {Francesco Ciraulo and Tatsuji Kawai and Samuele Maschio},
journal= {arXiv preprint arXiv:1812.09190},
year = {2018}
}