Related papers: One topos, many sites
The topological organization of several world cities are studied according to respective representations by complex networks. As a first step, the city maps are processed by a recently developed methodology that allows the most significant…
Through the subsequent discussion we consider a certain particular sort of (topological) algebras, which may substitute the `` structure sheaf algebras'' in many--in point of fact, in all--the situations of a geometrical character that…
This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…
We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…
There is an interplay between models, specified by variables and equations, and their connections to one another. This dichotomy should be reflected in the abstract as well. Without referring to the models directly -- only that a model…
Using Butz and Moerdijk's topological groupoid representation of a topos with enough points, a `syntax-semantics' duality for geometric theories is constructed. The emphasis is on a logical presentation, starting with a description of the…
We present and characterize the classes of Grothendieck toposes having enough supercompact objects or enough compact objects. In the process, we examine the subcategories of supercompact objects and compact objects within such toposes and…
We extend Deligne's original argument showing that locally coherent topoi have enough points, clarified using collage diagrams. We show that our refinement of Deligne's technique can be adapted to recover every existing result of this kind,…
We elaborate on the representation theorems of topoi as topoi of discrete actions of various kinds of localic groups and groupoids. We introduce the concept of "proessential point" and use it to give a new characterization of pointed Galois…
We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…
We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are…
What is the role of topos theory in the topos models for quantum theory as used by Isham, Butterfield, Doring, Heunen, Landsman, Spitters and others? In other words, what is the interplay between physical motivation for the models and the…
We extend the notion of algebraic stack to an arbitrary subcanonical site C. If the topology on C is local on the target and satisfies descent for morphisms, we show that algebraic stacks are precisely those which are weakly equivalent to…
The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can further the study of quantum logic and give rise to new…
Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be…
We study various characterizations of higher sites over a given $\infty$-category $\mathcal{C}$ which are conceptually in line with their classical ordinary categorical counterparts, and extract some new results about $\infty$-topos theory…
We give a short, mostly elementary and self-contained proof of the classical result that the groups of diffeomorphisms, homeomorphisms, and homotopy equivalences of a surface have the same group of connected components.
Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…
This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between…