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 characterised `pointwise'. We also show that the co-frame operations on the co-frame of internal sublocales admit a `pointwise' description too.
Keywords: Internal locale, internal nucleus, Grothendieck topos
2020 MSC: 18B25 (Primary), 18F70 (Secondary)
Theory and Applications of Categories, Vol. 41, 2024, No. 35, pp 1160-1202.
Published 2024-09-23.
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