Some Properties of Internal Locale Morphisms Externalised
Algebraic Geometry
2026-03-17 v2 Category Theory
Abstract
We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as sheaves and natural transformations. We characterise those morphisms of internal locales that induce surjective geometric morphisms and geometric embeddings, demonstrating that both can be computed `pointwise'. We also show that the co-frame operations on the co-frame of internal sublocales can also be computed `pointwise' too.
Cite
@article{arxiv.2301.00961,
title = {Some Properties of Internal Locale Morphisms Externalised},
author = {Joshua Wrigley},
journal= {arXiv preprint arXiv:2301.00961},
year = {2026}
}
Comments
46 pages. Updated version for submission. New sections on examples and applications, in addition to general improvements