Subject: request post to AT list Date: Thu, 19 Jun 2003 15:00:05 -0400 (EDT) From: Stefan Forcey To: dmd1@lehigh.edu Dr. Davis, I must take the opportunity to thank you again for the hospitality shown by you and your wife this past weekend. I hope to make the Lehigh conference a regular. Here is a pair of abstracts for some preprints of interest to people in homotopy theory and n-category theory. If you can post them to the list you moderate that would be wonderful. Thanks, Stefan Forcey http://arxiv.org/abs/math.CT/0306086 From: Stefan Forcey Enrichment as Categorical Delooping I: Enrichment Over Iterated Monoidal Categories The 2-category V-Cat of categories enriched over a braided monoidal category V is not itself braided in any way that is based upon the braiding of V. The exception is the case in which V is symmetric, which leads to V-Cat being symmetric as well. This paper describes how these facts are related to a categorical analogue of topological delooping. It seems that the analogy of loop spaces is a good guide for how to define the concept of enrichment over various types of monoidal objects, including k-fold monoidal categories and their higher dimensional counterparts. The main result is that for V a k-fold monoidal category, V-Cat becomes a (k-1)-fold monoidal 2-category in a canonical way. I indicate how this process may be iterated by enriching over V-Cat, along the way defining the 3-category of categories enriched over V-Cat. http://arxiv.org/abs/math.CT/0306086 From: Stefan Forcey Higher Dimensional Enrichment Lyubashenko has described enriched 2-categories as categories enriched over V-Cat, the 2-category of categories enriched over a symmetric monoidal V. I have generalized this to the k-fold monoidal V. The symmetric case can easily be recovered. This paper reviews the morphisms of V-2-categories and gives the details of the proof that these form the structure of a 3-category.