TY - JOUR
T1 - The low-dimensional structures formed by tricategories
AU - Garner, Richard
AU - Gurski, Nick
N1 - 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.
PY - 2009/5
Y1 - 2009/5
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=68349144649&partnerID=8YFLogxK
U2 - 10.1017/S0305004108002132
DO - 10.1017/S0305004108002132
M3 - Article
AN - SCOPUS:68349144649
SN - 0305-0041
VL - 146
SP - 551
EP - 589
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 3
ER -