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Oxford Quantum Talks Archive

The periodic table of n-categories

Eugenia Cheng, University of Sheffield
Categories, Logic and Foundations of Physics IV, January 2009, Imperial College London

Degenerate n-categories are those whose lowest k dimensions are trivial, for some k>0. These can be thought of as the categorical analogue of loop spaces. The resulting multiplicative structures are interesting in their own right, and fit into a table known as the ''periodic table of n-categories''. The table has various interesting patterns observable in low-dimensions and conjectured in general by Baez and Dolan. The structures that arise in this way include monoids and commutative monoids, as well as monoidal, braided, and symmetric monoidal categories. We will outline the main ideas behind the Periodic Table, its patterns and predictions, including the crucial stabilisation property which lead Baez and Dolan to conjecture a beautiful universal property to characterise higher-dimensional tangles. The talk will be introductory, in some sense a sequel to Tom Leinster's introduction to n-categories that precedes it. Beyond this no knowledge of n-categories will be assumed.

[video] [streaming video] [slides]