Related papers: Various topos of types constructions
We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of…
This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…
We construct a topology on a given algebraically closed field with a distinguished subfield which is also algebraically closed. This topology is finer than Zariski topology and it captures the sets definable in the pair of algebraically…
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.
We present various constructions of sequences of polynomials satisfying the Binomial Theorem in finite characteristic based on the theory of additive polynomials. Various actions on these constructions are also presented. It is an open…
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
Mimicking Ogus's construction, we define a site, for varieties over a field of char. p > 0, using Monsky--Washnitzer algebras/weak formal schemes. We prove a comparison theorem between the MW cohomology and a certain analytic cohomology.
The notion of geometric construction is introduced. This notion allows to compare incidence configurations in the algebraic and tropical plane. We provide an algorithm such that, given a tropical instance of a geometric construction, it…
A new algebraic treatment of dependent type theory is proposed using ideas derived from topos theory and algebraic set theory.
We introduce toric arrangements, essentially finite families of codimension 1 subtori of a torus or of their cosets, as a periodic generalization of hyperplane arrangements, compute cohomology of the complement of such an arrangement and…
In this chapter we propose Generic Ontology Design Patterns, GODPs, as a methodology for representing and instantiating ontology design patterns in a way that is adaptable, and allows domain experts (and other users) to safely use them…
We confirm a conjecture of Monical, Tokcan and Yong on a characterization of the lattice points in the Newton polytopes of key polynomials.
We study toposes of actions of monoids on sets. We begin with ordinary actions, producing a class of presheaf toposes which we characterize. As groundwork for considering topological monoids, we branch out into a study of supercompactly…
We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb…
We briefly review the origins and development of Borsuk's Theory of Shapes and the Multivalued Shape of Sanjurjo. We use a construction over metric compacta using hyperspaces to define a finite type version.
We study the weighted Fock spaces in one and several complex variables. We evaluate the dimension of these spaces in terms of the weight function extending and completing earlier results by Rozenblum-Shirokov and Shigekawa.
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
This article provides a complete characterization of the conformal classes of product tori and standard flat tori in complex dimension 1 (real dimension 2). Utilizing basic differential geometry methods, our approach contrasts with…