The low-dimensional structures formed by tricategories

Richard Garner; Nick Gurski

doi:10.1017/S0305004108002132

The low-dimensional structures formed by tricategories

Richard Garner^*, Nick Gurski

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

36 Downloads (Pure)

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.

Original language	English
Pages (from-to)	551-589
Number of pages	39
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	146
Issue number	3
DOIs	https://doi.org/10.1017/S0305004108002132
Publication status	Published - May 2009
Externally published	Yes

Bibliographical note

Copyright [2009] Cambridge Philosophical Society. Published by Cambridge University Press. Article originally published in [Garner R and Gurski N. "The low-dimensional structures formed by tricategories." Math. Proc. Camb. Phil. Soc. (2009), 146, 551]. The original article can be found at http://dx.doi.org/10.1017/S0305004108002132.

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title = "The low-dimensional structures formed by tricategories",

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AB - 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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The low-dimensional structures formed by tricategories

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