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The low-dimensional structures formed by tricategories

Published online by Cambridge University Press:  01 May 2009

RICHARD GARNER  and
NICK GURSKI
RICHARD GARNER
Affiliation:
Department of Mathematics, Uppsala University, Box 480, S-751 06 Uppsala, Sweden. e-mail: richard@math.uu.se
NICK GURSKI
Affiliation:
Department of Mathematics, Yale University, 10 Hillhouse Avenue, PO Box 208283, New Haven, CT 06520-8283, U.S.A. e-mail: michaeln.gurski@yale.edu
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 3 , May 2009 , pp. 551 - 589
Copyright
Copyright © Cambridge Philosophical Society 2009

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