Related papers: Sheaves and conditional sets
We develop a theory of sheaves and cohomology on the category of proper modulus pairs. This complements [KMSY21], where a theory of sheaves and cohomology on the category of non-proper modulus pairs has been developed.
We describe right-hand skew Boolean algebras in terms of a class of presheaves of sets over Boolean algebras called Boolean sets, and prove a duality theorem between Boolean sets and etale spaces over Boolean spaces.
Learning transferable knowledge across similar but different settings is a fundamental component of generalized intelligence. In this paper, we approach the transfer learning challenge from a causal theory perspective. Our agent is endowed…
Complex systems of systems (SoS) are characterized by multiple interconnected subsystems. Typically, each subsystem is designed and analyzed using methodologies and formalisms that are specific to the particular subsystem model of…
We define an equivalence relation among coherent sheaves on a projective variety called biliaison. We prove the existence of sheaves that are minimal in a biliaison class in a suitable sense, and show that all sheaves in the same class can…
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
Human beings learn causal models and constantly use them to transfer knowledge between similar environments. We use this intuition to design a transfer-learning framework using object-oriented representations to learn the causal…
The goal of this note is to provide a constructive version of the proof of local structure of etale algebras.
In this paper, we investigate the order algebraic structure in the category of sheaves on a given locale $X$. Since every localic topos has a generating set formed by its subterminal objects, we define a "point" of a partially ordered sheaf…
The purpose of this paper is to explain how the identities of various fundamental lemmas fall within the scope of the transfer principle, a general result that allows to transfer theorems about identities of p-adic integrals from one…
A sensor integration framework should be sufficiently general to accurately represent all information sources, and also be able to summarize information in a faithful way that emphasizes important, actionable information. Few approaches…
We develop a theory of residues for arithmetic surfaces, establish the reciprocity law around a point, and use the residue maps to explicitly construct the dualizing sheaf of the surface. These are generalisations of known results for…
The aim of this paper is to present a very simple set of conditions, necessary for the management of knowledge of a poset $T$ of two agents, which are partially ordered by the capabilities available in the system. We build up a formal…
An \'etale structure over a topological space $X$ is a continuous family of structures (in some first-order language) indexed over $X$. We give an exposition of this fundamental concept from sheaf theory and its relevance to countable model…
This is the second in a series of papers on the relation between algebraic set theory and predicative formal systems. In part I, we introduced the notion of a predicative category of small maps and obtained the result that such categories…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
The coset construction is the most important tool to construct rational conformal field theories with known chiral data. For some cosets at small level, so-called maverick cosets, the familiar analysis using selection and identification…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
The Sheaf-Theoretic Contextuality (STC) theory developed by Abramsky and colleagues is a very general account of whether multiply overlapping subsets of a set, each of which is endowed with certain "local'" structure, can be viewed as…
We apply constructions from topos-theoretic approaches to quantum theory to algebraic quantum field theory. Thus a net of operator algebras is reformulated as a functor that maps regions of spacetime into a category of ringed topoi. We ask…