Geodesic
Some properties of internal locale morphisms externalised
Theory and applications of categories, Tome 41 (2024), pp. 1160-1202

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Publié le :
Classification : 18B25 (Primary), 18F70 (Secondary)
Keywords: Internal locale, internal nucleus, Grothendieck topos 
@article{TAC_2024_41_a34,
     author = {Joshua L. Wrigley},
     title = {Some properties of internal locale morphisms externalised},
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     publisher = {mathdoc},
     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a34/}
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Joshua L. Wrigley. Some properties of internal locale morphisms externalised. Theory and applications of categories, Tome 41 (2024), pp. 1160-1202. http://geodesic.mathdoc.fr/item/TAC_2024_41_a34/