%0 Generic %1 garner2007lowdimensional %A Garner, Richard %A Gurski, Nick %D 2007 %K category tricategory %R 10.1017/S0305004108002132 %T The low-dimensional structures formed by tricategories %U http://arxiv.org/abs/0711.1761 %X 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.

@misc{garner2007lowdimensional, 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.}, added-at = {2015-01-06T08:05:40.000+0100}, author = {Garner, Richard and Gurski, Nick}, biburl = {https://www.bibsonomy.org/bibtex/2700fa9c80665eed0e440517d71ec41eb/t.uemura}, description = {[0711.1761] The low-dimensional structures formed by tricategories}, doi = {10.1017/S0305004108002132}, interhash = {adf47b68781d425b9db881840590810f}, intrahash = {700fa9c80665eed0e440517d71ec41eb}, keywords = {category tricategory}, note = {cite \href{http://arxiv.org/abs/0711.1761}{arxiv:0711.1761}Comment: 41 pages; v2: final journal version}, timestamp = {2015-01-06T08:05:40.000+0100}, title = {The low-dimensional structures formed by tricategories}, url = {http://arxiv.org/abs/0711.1761}, year = 2007 }