Pour le prochain séminaire de l'équipe Cosynus, nous aurons le plaisir d'accueillir Maxime Lucas qui parlera des liens entre réécriture et homotopie.
Résumé: Rewriting theory is traditionally used to study the decidability of equality in various objects. In a seminal paper, Squier made a link between a monoid admitting a presentation which is well-behaved from a rewriting point of view (terminating and confluent in particular), and homotopical properties of this monoid. From this stemmed higher dimensional rewriting theory, which consists in a range of techniques aiming to deduce homotopical information on an object using a well-behaved presentation of this object.
In this talk, we give a general presentation of higher dimensional rewriting applied to monoid and other structures (such as algebras, operads, etc.). We show that (strict) cubical omega-categories form a natural setting in which to express the constructions of higher-dimensional rewriting. In particular, we link the good homotopical properties of the Gray tensor product of cubical omega-categories to the algebraic structure of the local branchings.