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Pasting in multiple categories

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Richard Steiner

In the literature there are several kinds of concrete and abstract cell
complexes representing composition in n-categories, \omega-categories
or \infty-categories, and the slightly more general partial
\omega-categories. Some examples are parity c omplexes, pasting schemes
and directed complexes. In this paper we give an axiomatic treatment: that
is to say, we study the class of `\omega-complexes' which consists of
all complexes representing partial \omega-categories. We show that
\omega-complexes can be given geometric structures and that in most
important examples they become well-behaved CW complexes; we characterise
\omega-complexes by conditions on their cells; we show that a product of
\omega-complexes is again an \omega-complex; and we describe some
products in detail.

Keywords: pasting diagram, n-category, .omega-category, infinite-category, partial omega-category,
parity complex, omega-complex, directed complex.

1991 MSC: 18D05.

*Theory and Applications of Categories*, Vol. 4, 1998, No. 1, pp 1-36.

http://www.tac.mta.ca/tac/volumes/1998/n1/n1.dvi

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