Geodesic
Pasting in multiple categories
Theory and applications of categories, Tome 4 (1998), pp. 1-36.

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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.
Classification : 18D05.
Keywords: pasting diagram, n-category, .omega-category, infinite-category, partial omega-category, parity complex, omega-complex, directed complex. 
@article{TAC_1998_4_a0,
     author = {Richard Steiner},
     title = {Pasting in multiple categories},
     journal = {Theory and applications of categories},
     pages = {1--36},
     publisher = {mathdoc},
     volume = {4},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_1998_4_a0/}
}
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Richard Steiner. Pasting in multiple categories. Theory and applications of categories, Tome 4 (1998), pp. 1-36. http://geodesic.mathdoc.fr/item/TAC_1998_4_a0/