A short course on infinity-categories

Details A short course on infinity-categories A short course on infinity-categories

2010-07-17

arxiv.org/abs/1007.2925v1

Mathematics

Algebraic Topology

53 pages

Scientific paper

These are notes on the theory of infinity-categories building on a series of talks given by the author in Warsaw in January, 2010. The aim is to give a non-technical introduction to some of the main ideas of the theory in order to facilitate the digestion of the far more voluminous tomes due to Andre Joyal and Jacob Lurie where the theory is developed in full detail. Besides the basic infinity-categorical notions, we mention the Joyal and Bergner model structures which are two approaches to the theory of (infinity,1)-categories. We then treat the theory of (symmetric) monoidal infinity-categories and introduce the notion of (commutative) algebra objects. We finish with a summary of Lurie's treatment of spectra and the smash product from the perspective of infinity-categories which allows us to give the definition of A-infinity and E-infinity ring spectra.

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