On Cyclic Star-Autonomous Categories
Abstract
We discuss cyclic star-autonomous categories; that is, unbraided star- autonomous categories in which the left and right duals of every object p are linked by coherent natural isomorphism. We settle coherence questions which have arisen concerning such cyclicity isomorphisms, and we show that such cyclic structures are the natural setting in which to consider enriched profunctors. Specifically, if V is a cyclic star-autonomous category, then the collection of V-enriched profunctors carries a canonical cyclic structure. In the case of braided star-autonomous categories, we discuss the correspondences between cyclic structures and balances or tortile structures. Finally, we show that every cyclic star-autonomous category is equivalent to one in which the cyclicity isomorphisms are identities.
Cite
@article{arxiv.1007.5099,
title = {On Cyclic Star-Autonomous Categories},
author = {Jeff Egger and Micah Blake McCurdy},
journal= {arXiv preprint arXiv:1007.5099},
year = {2010}
}
Comments
28 pages, a variety of figures. Submitted for publication in the "CT2010" Special Volume of the Journal of Pure and Applied Algebra