00:00:00 / 00:00:00

Categorification of Rule Algebras

De Nicolas Behr

Apparaît dans la 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.

Informations sur la vidéo

  • Date de captation 28/11/2022
  • Date de publication 30/11/2022
  • Institut IHES
  • Langue Anglais
  • Audience Chercheurs
  • Format MP4

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow




Inscrivez-vous

  • Mettez des vidéos en favori
  • Ajoutez des vidéos à regarder plus tard &
    conservez votre historique de consultation
  • Commentez avec la communauté
    scientifique
  • Recevez des notifications de mise à jour
    de vos sujets favoris
Donner son avis