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.