Multiple categories: The equivalence of a globular and a cubical approach. (English) Zbl 1013.18003
C. B. Spencer [Cah. Topol. Géom. Différ. Catégoriques 18, 409-429 (1977; Zbl 0378.18008)] stated that the category of 2-categories and the category of double categories with connection were equivalent; a detailed proof was provided by R. Brown and G. H. Mosa [Theory Appl. Categ. 5, 163-175 (1999; Zbl 0918.18005)]. The present paper extends the notion of connection on a double category to infinite dimensions and proves the category of such equivalent to the category of (strict) \(\omega\)-categories.
Reviewer: Ross H.Street (North Ryde)
MSC:
| 18D05 | Double categories, \(2\)-categories, bicategories and generalizations (MSC2010) |
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