Stéphane Gaussent (Université Nancy 1), Coherent presentations and actions on categories


  • Feb. 28, 2012, 16:30 - 17:30


I will report on a joint work with Yves Guiraud and Philippe Malbos. For a given presentation of a monoid M, we consider its associated 2-polygraph. Then using a machinery based on higher rewriting theory, we obtain a homotopy basis. This homotopy basis is exactly the piece of information one needs to get the coherence diagrams involved in a (clever) definition of an action of M on a category. In some good cases, it is possible to simplify this basis. Namely, if we start with the Deligne's presentation of the positive braid monoid, we obtain a simplified version of a result of Deligne.