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arXiv · 0711.1761

The low-dimensional structures formed by tricategories

Richard Garner·Nick Gurski
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Abstract

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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Richard Garner, Nick Gurski. 2011-10-14. The low-dimensional structures formed by tricategories. https://doi.org/10.1017/s0305004108002132

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