The low-dimensional structures formed by tricategories

Details The low-dimensional structures formed by tricategories The low-dimensional structures formed by tricategories

2007-11-12

arxiv.org/abs/0711.1761v2

Mathematical Proceedings of the Cambridge Philosophical Society 146 (2009), no. 3, pages 551-589

Mathematics

Category Theory

41 pages; v2: final journal version

Scientific paper

10.1017/S0305004108002132

We form tricategories and the homomorphisms between them into a bicategory, whose 2-cells are certain degenerate tritransformations. We then enrich this bicategory into an example of a three-dimensional structure called a locally cubical bicategory, this being a bicategory enriched in the monoidal 2-category of pseudo double categories. Finally, we show that every sufficiently well-behaved locally cubical bicategory gives rise to a tricategory, and thereby deduce the existence of a tricategory of tricategories.

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