We construct a star-autonomous structure on the functor category $K^J$, where $J$ is small, $K$ is small-complete, and both are star-autonomous. A weaker result, that $K^J$ admits a linear distributive structure, is also shown under weaker hypotheses. The latter leads to a deeper understanding of the notion of linear functor.
Keywords: Linear distributive categories, star-autonomous categories, functor categories
2000 MSC: 18D10,18D15
Theory and Applications of Categories,
Vol. 20, 2008,
No. 11, pp 307-333.
http://www.tac.mta.ca/tac/volumes/20/11/20-11.dvi
http://www.tac.mta.ca/tac/volumes/20/11/20-11.ps
http://www.tac.mta.ca/tac/volumes/20/11/20-11.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/11/20-11.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/11/20-11.ps