We develop a notion of iterated monoidal category and show that this notion
corresponds in a precise way to the notion of iterated loop space. Specifically
the group completion of the nerve of such a category is an iterated loop space
and free iterated monoidal categories give rise to finite simplicial operads of
the same homotopy type as the classical little cubes operads used to
parametrize the higher H-space structure of iterated loop spaces. Iterated
monoidal categories encompass, as a special case, the notion of braided tensor
categories, as used in the theory of quantum groups.Comment: 55 pages, 3 PostScript figure