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Oxford Quantum Talks Archive

Infinity categories and infinity operads

Ieke Moerdijk, Utrecht University
Categories, Logic and Foundations of Physics IV, January 2009, Imperial College London

We discuss some aspects of the simplicial theory of infinity-categories which originates with Boardman and Vogt, and has recently been developed by Joyal, Lurie and others. The main purpose of the talk will be to present an extension of this theory which covers infinity-operads. It is based on a modification of the notion of simplicial set, called “dendroidal set”. One of the main results is that the category of dendroidal sets carries a monoidal Quillen model structure, in which the fibrant objects are precisely the infinity-operads, and which contains the Joyal model structure for infinity-categories as a localization. The lecture is partly based on joint work with Ittay Weiss, Clemens Berger, and Denis-Charles Cisinski.

[video] [streaming video]