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Fibred sites and existential toposes

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arxiv 2212.11693 v1 pith:YWGUXLQX submitted 2022-12-22 math.AG math.CTmath.LO

Olivia Caramello This is my paper · ORCID
classification math.AGmath.CTmath.LO
keywords fibredtoposesexistentialsitesitestoposbuiltlocales
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In the context of relative topos theory via stacks, we introduce the notion of existential fibred site and of existential topos of such a site. These notions allow us to develop relative topos theory in a way which naturally generalizes the construction of toposes of sheaves on locales, and also provides a framework for investigating the connections between Grothendieck toposes as built from sites and elementary toposes as built from triposes. Then we focus on fibred preorder sites and establish a fibred generalisation of the ideal-completion of a preorder site. Lastly, we provide an explicit description of the hyperconnected-localic factorization of a geometric morphism in terms of internal locales.

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  1. Local fibrations and morphisms of relative toposes

    math.CT 2025-07 conditional novelty 6.0 of 10

    Local fibrations, defined using Grothendieck topologies, characterize the site-level functors that give morphisms of relative toposes and support a weak indexed Diaconescu theorem.

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