7 papers
De Morgan's law in toposes I
Olivia Caramello, Yorgo Chamoun
We study toposes satisfying De Morgan's law, in particular we give characterizations of geometric theories whose classifying topos is De Morgan, clarifying the link with the amalga…
On fibred products of toposes
Léo Bartoli, Olivia Caramello
In the setting of relative topos theory, we show that the pullback of a relative presheaf topos on an arbitrary fibration is the relative presheaf topos on its inverse image. To th…
Morphisms and comorphisms of sites II -- Distributors of sites
Axel Osmond, Olivia Caramello
We introduce a notion of distributor of sites, involving suited analogs of flatness and cover-preservation, and show that this notion jointly generalizes those of morphism and como…
Sheaves on a bicategory
Olivia Caramello, Elio Pivet
We give a detailed account of the theory of enrichment over a bicategory and show that it establishes a two-fold generalization of enrichment over both quantaloids and monoidal cat…
Local fibrations and morphisms of relative toposes
Léo Bartoli, Olivia Caramello
We introduce the notion of local fibration, a generalization of the notion of fibration which takes into account the presence of Grothendieck topologies on the two categories, and…
Morphisms and comorphisms of sites I -- Double categories of sites
Olivia Caramello, Axel Osmond
We arrange morphisms and comorphisms of sites as the horizontal and vertical cells of a double category of sites; using the formalism of extensions and restrictions of presheaves,…