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Categorification of Rule Algebras

By Nicolas Behr

Appears in collection : Combinatorics and Arithmetic for Physics : Special Days

Reporting on joint work in progress with P.-A. Melliès and N. Zeilberger, I will present a novel approach to formalize operations in compositional rewriting sys- tems wherein the number of ways to apply a rewrite is of interest. The approach is based upon defining a suitable double category to capture individual rewriting steps as its 2-cells, requiring in addition certain fibrational properties to hold for the functors of vertical source and target as well as of horizontal composition of cells. Counting numbers of realizations of individual rewriting steps or sequences rewrites is then implemented via a presheaf calculus over 2-cells. I will demon- strate how the notion of rule algebra representations is captured in this calculus and how the rule algebras themselves are categorified via a categorical construc- tion involving coends.

Information about the video

  • Date of recording 11/28/22
  • Date of publication 11/30/22
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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