### 27.04.14 - 02.05.14, Seminar 14182

# Categorical Methods at the Crossroads

### The following text appeared on our web pages prior to the seminar, and was included as part of the invitation.

## Motivation

Since the 1960s, category theory has been recognised as a powerful conceptual framework and a flexible specification language. The range of research areas where categorical methods found application is quite wide: from physics, economics, and linguistics to many branches of mathematics, especially algebraic geometry, algebraic topology, and logic. And, of course, computer science: possibly the discipline, apart from mathematics, where these methods have been most wholeheartedly adopted. Indeed, they have become part of the standard “tool-box” in many areas of theoretical informatics, from programming languages to automata, from process calculi to type theory.

Despite their flexibility and expressiveness, a more general acceptance of categorical methods has been hindered by the perceived difficulties of the formalism. As a consequence, many researchers in different communities share the feeling of under-exploitation of the potentialities of category theory to their areas of interest. The seminar proposes to bring together people from various disciplines that are interested in the application of categorical tools in their research area, moving from computer science towards venues such as economics, mathematics, and physics.

Topics for the workshop include quantum computing, mathematical physics, distributed and concurrent systems, programming languages and models, rewriting, modal and first-order logics, (co)algebraic specifications (and non-well founded sets), reflexive economics, epistemic game theory, automata theory, and visual languages. Some of these items span more than one discipline, e.g. game theory, and the list is far from exhaustive. Although the scope of the meeting is broad, the over-arching research theme is to develop categorical methods as a unified approach to the modelling of complex systems.

Despite the relevance of each research topic, and the benefits to their understanding that may come from a plurality of voices in a discussion, the seminar will indeed address more general concerns. As far as each single discipline is concerned, the workshop should help the reconciliation of the research strands that are using categorical tools. Most importantly though, the meeting should aim at building bridges between disciplines, by checking the variety of uses of categorical methods in different fields and trying to find common abstractions that allow the same structures and concepts to be recognized as they arise in very different settings, and to be transferred from one area to another.

The overall purpose of this Dagstuhl Perspectives Workshop would then be to start developing a coherent research community applying categorical methods to a wide range of disciplines. The common mathematical language and concepts can provide a basis for fruitful cross-disciplinary interactions by fostering cross-fertilisation and facilitating “technology transfer”, locating synergies and exploring new directions, thus helping to build a modern structural applied mathematics fit for the 21st century.