相关论文: Operational Theories of Physics as Categories

Many insights into the quantum world can be found by studying it from amongst more general operational theories of physics. In this thesis, we develop an approach to the study of such theories purely in terms of the behaviour of their…

This thesis develops the theory of effectuses as a categorical axiomatic approach to quantum theory. It provides a comprehensive introduction to effectus theory and reveals its connections with various other topics and approaches.

We argue that category theory should become a part of the daily practice of the physicist, and more specific, the quantum physicist and/or informatician. The reason for this is not that category theory is a better way of doing mathematics,…

We undertake a reconstruction of the epistemic significance of research on operational theories in quantum foundations. We suggest that the space of operational theories is analogous to the space of possible worlds employed in the possible…

Category theory has become central to certain aspects of theoretical physics. Bain [Synthese, 190:1621--1635 (2013)] has recently argued that this has significance for ontic structural realism. We argue against this claim. In so doing, we…

We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM…

Measures in the context of Category Theory lead to various relations, even differential relations, of categories that are independent of the mathematical structure forming objects of a category. Such relations, which are independent of…

In this work, we give rigorous operational meaning to superposition of causal orders. This fits within a recent effort to understand how the standard operational perspective on quantum theory could be extended to include indefinite…

A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties…

Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases. Predicates in effectus theory are not subobjects having a Heyting algebra…

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills…

We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…

The basic concepts of category theory are developed and examples of them are presented to illustrate them using measurement theory and probability theory tools. Motivated by Perrone's workarXiv:1912.10642 where notes on category theory are…

This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…

The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive…

In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…

An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…

This paper charts a very direct path between the categorical approach to quantum mechanics, due to Abramsky and Coecke, and the older convex-operational approach based on ordered vector spaces (recently reincarnated as "generalized…

In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing…

We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first…