Related papers: Categor\'ias. Los 30 primeros a\~nos
We prove a stronger version of the octahedral axiom in a pre-triangulated category. The proof uses a new lemma about exact sequences in pointed additive categories which is based on a weak converse of the snake lemma.
Context is a rich concept and is an elusive concept to define. The concept of context has been studied by philosophers, linguists, psychologists, and recently by computer scientists. Within each research community the term context was…
Locales have been studied as "topologies without points", mainly by tools of category theory. While traditional topology presents a space as a set of points with specified neighborhoods, localic topology presents a space as a lattice of…
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…
Some ideas aimed to understand that time is one-dimensional are briefly reviewed. Some attempts to construct theories in varieties with more spatial and temporal components are presented. It is discussed, from the epistemological point of…
Understanding the creation, evolution, and dissemination of scientific knowledge is crucial for bridging diverse subject areas and addressing complex global challenges such as pandemics, climate change, and ethical AI. Scientometrics, the…
Competitive debaters often find themselves facing a challenging task -- how to debate a topic they know very little about, with only minutes to prepare, and without access to books or the Internet? What they often do is rely on "first…
This survey presents an overview of integrating prior knowledge into machine learning systems in order to improve explainability. The complexity of machine learning models has elicited research to make them more explainable. However, most…
Presents a history of the evolution of the author's ideas on program-size complexity and its applications to metamathematics over the course of more than four decades. Includes suggestions for further work.
$E$-theory was originally defined concretely by Connes and Higson and further work followed this construction. We generalise the definition to $C^\ast$-categories. $C^\ast$-categories were formulated to give a theory of operator algebras in…
We introduce HyperLex - a dataset and evaluation resource that quantifies the extent of of the semantic category membership, that is, type-of relation also known as hyponymy-hypernymy or lexical entailment (LE) relation between 2,616…
In a recent paper by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects in…
Quantum information is an emerging field which has attracted a lot of attention in the last fifteen years or so. It is a broad subject which covers from the most applied questions (e.g., how to build quantum computers or secure…
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…
This is a review article on modular categories, extending an invited talk given at the workshop "Categorical (co)algebraic methods in quantum informatics and linguistics", Oxford, October 29-31, 2010. To appear in C. Heunen, M. Sadrzadeh,…
In this manuscript various components of research are listed and briefly discussed. The topics considered in this write-up cover a part of the research methodology paper of Master of Philosophy (M.Phil.) course and Doctor of Philosophy…
In this article, we propose a Category Theory approach to (syntactic) interoperability between linguistic tools. The resulting category consists of textual documents, including any linguistic annotations, NLP tools that analyze texts and…
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…
While large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, current benchmarks fail to adequately measure library-grounded abstraction -- the ability to reason with high-level interfaces and…
We introduce some classes of genuine higher categories in homotopy type theory, defined as well-behaved subcategories of the category of types. We give several examples, and some techniques for showing other things are not examples. While…