Pasting in multiple categories
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.
Theory and Applications of Categories, Vol. 4, 1998, No. 1, 1-36
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