3 citations · 4 across the 9 of their papers we have counts for
11 papers
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…
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,…
On a (terminally connected, pro-etale) factorization of geometric morphisms
Olivia Caramello, Axel Osmond
We extend the classical (connected, etale) factorization of locally connected geometric morphisms into a (terminally connected, pro-etale) factorization for all geometric morphisms…
Codescent and bicolimits of pseudo-algebras
Axel Osmond
We categorify cocompleteness results of monad theory, in the context of pseudomonads. We first prove a general result establishing that, in any 2-category, weighted bicolimits can…
Bi-accessible and bipresentable 2-categories
Ivan Di Liberti, Axel Osmond
We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of…
Local right biadjoints, bistable pseudofunctors and 2-geometries for Grothendieck topoi
Axel Osmond
We provide bicategorical analogs of several aspects of the notion of geometry in the sense of the theory of spectrum. We first introduce a notion of local right biadjoint, and prov…
On coslices and commas of locally finitely presentable categories
Axel Osmond
We give an explicit description of the generator of finitely presented objects of the coslice of a locally finitely presentable category under a given object, as consisting of all…
The over-topos at a model
Olivia Caramello, Axel Osmond
With a model of a geometric theory in an arbitrary topos, we associate a site obtained by endowing a category of generalized elements of the model with a Grothendieck topology, whi…
The spectral site revisited
Axel Osmond
We give the site-theoretic account of the spectral construction as first introduced by Coste. We provide a detailed examination of the geometric properties of the spectrum, in part…
On Diers theory of Spectrum II: Geometries and dualities
Axel Osmond
This second part comes to the construction of the spectrum associated to a situation of multi-adjunction. Exploiting a geometric understanding of its multi-versal property, the spe…
On Diers theory of Spectrum I : Stable functors and right multi-adjoints
Axel Osmond
Diers developed a general theory of right multi-adjoint functors leading to a purely categorical, point-set construction of spectra. Situations of multiversal properties return set…