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arXiv · 1907.05104

Artin glueings of frames as semidirect products

Peter F. Faul·Graham R. Manuell
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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.

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Peter F. Faul, Graham R. Manuell. 2019-07-11. Artin glueings of frames as semidirect products. https://doi.org/10.1016/j.jpaa.2020.106334

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