Nicolas Behr, IRIF Paris
Category-theoretical rewriting theory 2.0: on rule algebras and tracelets
Traditionally, rewriting theories over adhesive categories have been developed predominantly within the computer science community, with a rich history of over 40 years. In this talk, I will present recent resuls on certain new structures in rewriting theories, which in particular permit to extend the domains of applicability of these theories to (bio-)chemistry, social sciences, combinatorics and many other fields. Based upon the discovery of a certain notion of associativity in sequential compositions of rewriting steps, rule algebras may be introduced as a mathematical structure encoding the combinatorics and non-determinism of sequential compositions. In conjunction with the representation theory of these associative, unital algebras, it is possible to develop the stochastic mechanics and combinatorics theory of rewriting in close analogy to well-established analogous concepts in mathematical physics. I will aim to provide an overview of the latest developments in this novel form of rewriting theory, including the recently introduced concept of tracelets as carriers of causal information in traces of sequential rule applications.