Only two SMC structures on Cat?
Power, A.J. and Robinson, E.P. Premonoidal categories and notions of computation (ftp://ftp.dcs.qmw.ac.uk/pub/lfp/edmundr/premoncat.ps.gz) in section 2 asserts that there is excatly one symmetric monoidal closed structure on Cat besides the cartesian one. Does anyone know [the location of] a proof? ---Jason
Jason C Reed writes:
Power, A.J. and Robinson, E.P. Premonoidal categories and notions of computation (ftp://ftp.dcs.qmw.ac.uk/pub/lfp/edmundr/premoncat.ps.gz) in section 2 asserts that there is excatly one symmetric monoidal closed structure on Cat besides the cartesian one. Does anyone know [the location of] a proof?
---Jason
It's Proposition 4 of: Foltz, Lair, and Kelly, Algebraic categories with few moniodal biclosed structures or none, J. Pure Appl. Alg. 17:171-177, 1980. Steve Lack.
F. Foltz, C. Lair and G.M. Kelly. Algebraic categories with few monoidal biclosed structures or none. Journal of Pure and Applied Algebra, 17: 171--177. Jason C Reed wrote:
Power, A.J. and Robinson, E.P. Premonoidal categories and notions of computation (ftp://ftp.dcs.qmw.ac.uk/pub/lfp/edmundr/premoncat.ps.gz) in section 2 asserts that there is excatly one symmetric monoidal closed structure on Cat besides the cartesian one. Does anyone know [the location of] a proof?
---Jason
-- Prof. David J. Pym Telephone: +44 (0)1 225 38 3246 Professor of Logic & Computation Facsimile: +44 (0)1 225 38 3493 University of Bath Email: d.j.pym@bath.ac.uk Bath BA2 7AY, England, U.K. Web: http://www.bath.ac.uk/~cssdjp
participants (3)
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D. J. Pym -
Jason C Reed -
Steve Lack