相关论文: Sheaves of Structures, Heyting-Valued Structures, …

An introduction is given to the logic of sheaves of structures and to set theoretic forcing constructions based on this logic. Using these tools, it is presented an alternative proof of the independence of the Continuum Hypothesis; which…

We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…

The aim of this paper is to give a unifying description of various constructions (subanalytic, semialgebraic, o-minimal site) using the notion of T-topology. We then study the category of T-sheaves.

Many complicated network problems can be easily understood on small networks. Difficulties arise when small networks are combined into larger ones. Fortunately, the mathematical theory of sheaves was constructed to address just this kind of…

In this article, the theory of sheaves is studied from a categorical point of view. This perspective vastly generalizes the usual theory of sheaves of sets to a more abstract setting which allows us to investigate the theory of sheaves with…

We introduce and develop the theory of metric sheaves. A metric sheaf $\A$ is defined on a topological space $X$ such that each fiber is a metric model. We describe the construction of the generic model as the quotient space of the sheaf…

We study sheaves in the context of a duality theory for lattice structure endowed with extra operations, and in the context of forcing in a topos. Using Sheaf duality theory of Comer for cylindric algebras, we give a representation theorem…

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…

We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…

A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…

We present a uniform theory of constructible sheaves on arbitrary schemes with coefficients in topological or even condensed rings. This is accomplished by defining lisse sheaves to be the dualizable objects in the derived infinity-category…

We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…

Continuation of algebraic structures in families of dynamical systems is described using category theory, sheaves, and lattice algebras. Well-known concepts in dynamics, such as attractors or invariant sets, are formulated as functors on…

We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…

We give a classification theorem for a relevant class of $t$-structures in triangulated categories, which includes in the case of the derived category of a Grothendieck category, the $t$-structures whose hearts have at most $n$ fixed…

We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…

We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…

We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincar\'e duality and hard Lefschetz theorem), and their relations and applications to integral…

In this paper, we identify some categorical structures in which one can model predicative formal systems: in other words, predicative analogues of the notion of a topos, with the aim of using sheaf models to interprete predicative formal…

The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…