TY - JOUR
T1 - On cyclic star-autonomous categories
AU - Egger, J. M.
AU - McCurdy, M. B.
PY - 2012/8
Y1 - 2012/8
N2 - We discuss . cyclic star-autonomous categories, that is, unbraided star-autonomouscategories in which the left and right duals of every object . p are linked by coherent natural families of isomorphisms. 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.
AB - We discuss . cyclic star-autonomous categories, that is, unbraided star-autonomouscategories in which the left and right duals of every object . p are linked by coherent natural families of isomorphisms. 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.
UR - http://www.scopus.com/inward/record.url?scp=84861462176&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2012.02.011
DO - 10.1016/j.jpaa.2012.02.011
M3 - Article
VL - 216
SP - 1706
EP - 1725
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 8-9
ER -