The low-dimensional structures formed by tricategories
The low-dimensional structures formed by tricategories
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三范畴构成的低维结构
DOI：
10.1017/s0305004108002132
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发表时间：
2007
影响因子：
0.8
通讯作者：
N. Gurski
中科院分区：
文献类型：
--
作者：
Richard Garner;N. Gurski
我们把三范畴及其之间的同态构成一个双范畴，其2-胞腔是某些退化的三变换。然后，我们丰富这个bicategory到一个三维结构的例子，称为局部立方bicategory，这是一个bicategory丰富的monoidal 2范畴的伪双重范畴。最后，我们证明了，每一个充分良好的局部立方双范畴产生一个三范畴，从而推导出存在一个三范畴的三范畴。
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.