Abstract

Following the foundational work of Joyal and Lurie, the theory of infinity-categories is now widely being used. There are two ways of extending the theory to “infinity-operads”, one of them [CM] based on the theory of dendroidal sets, the other [HA] on the theory of cocartesian fibrations between infinity-categories, and ever since the appearance of the first versions of [HA] it was conjectured that the two theories are equivalent. In this lecture I will present an outline of a proof of this conjecture [HHM].

[CM] D.-C. Cisinski, I. Moerdijk, Dendroidal sets as models for homotopy operads, Journal of Topology 2011 [HA] J. Lurie, Higher Algebra, book available at http://www.math.harvard.edu/~lurie/ [HMM] G. Heuts, V. Hinich, I. Moerdijk, The equivalence of the dendroidal model and Lurie’s model for infinity operads, in preparation.