相关论文: Proceedings Applied Category Theory 2019
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
The aim of this paper is to reformulate the theory of unbounded derived categories, including more recent categories of first and second kind, using the language of $(\infty,1)$-categories.
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics,…
This is the arXiv index for the electronic proceedings of GD 2019, which contains the peer-reviewed and revised accepted papers with an optional appendix. Proceedings (without appendices) are also to be published by Springer in the Lecture…
We report on our experience implementing category theory in Coq 8.5. The repository of this development can be found at https://bitbucket.org/amintimany/categories/. This implementation most notably makes use of features, primitive…
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the primary purpose is to provide an ample supply of problems for…
This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…
This book provides an inviting tour through sheaf theory, from the perspective of applied category theory and pitched at a less specialized audience than is typical with introductions to sheaves. The book makes it as easy as possible for…
This volume constitutes the pre-proceedings of the DECLARE 2019 conference, held on September 9 to 13, 2019 at the University of Technology Cottbus - Senftenberg (Germany). Declarative programming is an advanced paradigm for the modeling…
These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind. There is no need to know advanced…
Overlay journals are characterised by their articles being published on open access repositories, often already starting in their initial preprint form as a prerequisite for submission to the journal prior to initiating the peer-review…
The quality of AI-generated output is often attributed to prompting technique, but extensive empirical observation suggests that context completeness may be more strongly associated with output quality. This paper introduces Context…
In this paper we propose a categorical theory of intensionality. We first revisit the notion of intensionality, and discuss we its relevance to logic and computer science. It turns out that 1-category theory is not the most appropriate…
We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces…
This dissertation builds a compositional cyber-physical systems theory to develop concrete semantics relating the above diverse views necessary for safety and security assurance. In this sense, composition can take two forms. The first is…
We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph rewriting. By examples, we show how this paradigm of software development makes it…
Peer-review plays a critical role in the scientific writing and publication ecosystem. To assess the efficiency and efficacy of the reviewing process, one essential element is to understand and evaluate the reviews themselves. In this work,…
AGI has become the Holly Grail of AI with the promise of level intelligence and the major Tech companies around the world are investing unprecedented amounts of resources in its pursuit. Yet, there does not exist a single formal definition…
The increasing prevalence of Artificial Intelligence (AI) in safety-critical contexts such as air-traffic control leads to systems that are practical and efficient, and to some extent explainable to humans to be trusted and accepted. The…
An effective structure helps an article to convey its core message. The optimal structure depends on the information to be conveyed and the expectations of the audience. In the current increasingly interdisciplinary era, structural norms…