Related papers: Category theory for scientists (Old version)
Category discovery (CD) is an emerging open-world learning task, which aims at automatically categorizing unlabelled data containing instances from unseen classes, given some labelled data from seen classes. This task has attracted…
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…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
Science is a fundamental human activity and we trust its results because it has several error-correcting mechanisms. Its is subject to experimental tests that are replicated by independent parts. Given the huge amount of information…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
Category Theory is a well-known powerful mathematical modeling language with a wide area of applications in mathematics and computer science, including especially the semantical foundations of topics in software science and development.…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Due to the lack of structured knowledge applied in learning distributed representation of categories, existing work cannot incorporate category hierarchies into entity information.~We propose a framework that embeds entities and categories…
We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…
Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…
We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…
Theoretical computer science discusses foundational issues about computations. It asks and answers questions such as "What is a computation?", "What is computable?", "What is efficiently computable?","What is information?", "What is…
This book is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory. A review of basic category theory is followed by a systematic discussion of 2-/bicategories, pasting diagrams, lax…
Artificial Intelligence (AI) has long pursued models, theories, and techniques to imbue machines with human-like general intelligence. Yet even the currently predominant data-driven approaches in AI seem to be lacking humans' unique ability…
This brief brochure is intended to present a philosophical theory known as relational materialism. We introduce the postulates and principles of the theory, articulating its ontological and epistemological content using the language of…
Based on Gandy's principles for models of computation we give category-theoretic axioms describing locally deterministic updates to finite objects. Rather than fixing a particular category of states, we describe what properties such a…
In designing an intelligent system that must be able to explain its reasoning to a human user, or to provide generalizations that the human user finds reasonable, it may be useful to take into consideration psychological data on what types…
In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs,…
We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power…
We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type…