Speaker
Paul-André Melliès (CNRS, Université Paris Cité, INRIA)
Title
The Rabbit Calculus: Convolution Products on Double Categories and Categorification of Rule Algebra
Abstract
Reporting on recent joint work with Nicolas Behr and Noam Zeilberger, I will describe the rabbit calculus, a convolution product over preasheaves of double categories motivated by term ad graph rewriting theory. As I will explain, the convolution product generalizes to every double category the usual Day tensor product of presheaves of monoidal categories. One interesting aspect of the construction is that this convolution product is in general only oplax associative. For that reason, several classes of double categories will be identified for which the convolution product is not just oplax associative, but fully associative. This includes in particular framed bicategories on the one hand, and double categories of term and graph rewriting theories on the other. For the latter, we establish a formula which justifies the view that the convolution product categorifies the rule algebra product, and captures the basic intuitions of causality in rewriting theory.
