Dimitri Ara (Univ Aix-Marseille), Street's orientals and Mac Lane's coherence theorem



In this talk, I will present some elements of the homotopy theory of strict n-categories, insisting on Street's orientals. The n-th oriental is a strict n-category shaped on the n-simplex. We will see that these objects govern higher associativities and in particular that Mac Lane's coherence theorem can be rephrased in terms of the combinatorics of low dimensional orientals. Using this setting and homotopical methods, I will sketch a proof of Mac Lane's coherence theorem. (This talk is based on joint work with Georges Maltsiniotis.)