The low-dimensional structures formed by tricategories

Richard Garner*, Nick Gurski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)
16 Downloads (Pure)


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 languageEnglish
Pages (from-to)551-589
Number of pages39
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
Publication statusPublished - May 2009
Externally publishedYes

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


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