Artin glueings of frames as semidirect products
Category Theory
2021-12-28 v2 General Topology
Abstract
Artin glueings provide a way to reconstruct a frame from a closed sublocale and its open complement. We show that Artin glueings can be described as the weakly Schreier split extensions in the category of frames with finite-meet preserving maps. These extensions correspond to meet-semilattice homomorphisms between frames, yielding an extension bifunctor. Finally, we discuss Baer sums, the induced order structure on extensions and the failure of the split short five lemma.
Keywords
Cite
@article{arxiv.1907.05104,
title = {Artin glueings of frames as semidirect products},
author = {Peter F. Faul and Graham R. Manuell},
journal= {arXiv preprint arXiv:1907.05104},
year = {2021}
}
Comments
12 pages. To be published in the Journal of Pure and Applied Algebra. Added more discussion about morphisms of split extensions