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Ubiquitous computing systems and the digital economy
Published in James Juniper, The Economic Philosophy of the Internet of Things, 2018
Category theory provides ubiquitous computing systems with a variety of formal approaches including the coalgebraic representation of automatons and transition systems, Domain theory, and the Geometry of Interaction, along with specific mathematical substrates such as the elementary topos. For its part, categorical logic links inferential procedures based on resource-using or linear logics with functional programming and algebraic topology, while string diagrams can represent everything from graphical linear algebra to signal flow graphs and topological quantum field theory (with the latter using string diagrams to account for the functional relationships holding between quantum phenomena and the cobordisms deriving from general relativity theory).
Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models
Published in Enterprise Information Systems, 2018
Set theory is a mathematical theory of collections of objects. Category theory is another fundamental and abstract mathematical theory, which can formalize many mathematical structures with a collection of objects and arrows (e.g., relations and functions). Although the authors are aware of long-lasting in-depth debate on the supremacy of these two theories, it is within the scope of this paper to state that set theory focuses on objects while category theory focuses not on objects, but on morphisms, i.e., arrows between the objects. Practically speaking, category theory is very sophisticated and difficult while set theory is easy and understandable with mathematics at the undergraduate level.
A mosaic of Chu spaces and Channel Theory I: Category-theoretic concepts and tools
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2019
Chris Fields, James F. Glazebrook
Category theory can be viewed as a unified language for handling conceptual complexities in both mathematics and computer science. Chu spaces and Chu flows provide a natural way of representing both the structure and processing of information and have been used to investigate the semantic foundations and design of data structures and programming languages. The examples that follow illustrate these applications and introduce concepts that will prove useful later.
Logical dual concepts based on mathematical morphology in stratified institutions: applications to spatial reasoning
Published in Journal of Applied Non-Classical Logics, 2019
The notions introduced here make use of basic notions of category theory (category, functors, natural transformations, etc.). We do not present these notions in these preliminaries, but interested readers may refer to textbooks such as Barr and Wells (1990), MacLane (1971).