On cyclic star-autonomous categories

J. M. Egger; M. B. McCurdy

doi:10.1016/j.jpaa.2012.02.011

On cyclic star-autonomous categories

J. M. Egger, M. B. McCurdy^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1706-1725
Number of pages	20
Journal	Journal of Pure and Applied Algebra
Volume	216
Issue number	8-9
DOIs	https://doi.org/10.1016/j.jpaa.2012.02.011
Publication status	Published - Aug 2012

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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.

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On cyclic star-autonomous categories

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