From: Mark Weber <mark.weber.math@googlemail.com>
To: selinger@mathstat.dal.ca (Peter Selinger)
Cc: ondrej.rypacek@gmail.com, categories@mta.ca (Categories List)
Subject: Re: Alternative closed structure on Cat
Date: Fri, 6 Jul 2012 09:42:09 +1000 [thread overview]
Message-ID: <E1Sn7pD-0004rg-CV@mlist.mta.ca> (raw)
In-Reply-To: <E1SmrWK-0001x4-8V@mlist.mta.ca>
Dear Ondrej and Peter
The fact to which Peter referred, that the tensor product in question
> is the unique other symmetric monoidal closed
> structure on Cat
was proved in the paper
[1] F. Foltz, G.M.Kelly, and C. Lair, "Algebraic categories with few biclosed monoidal structures or none", JPAA 17:171-177, 1980
As for the name, this tensor product has been called the "funny tensor product" by some authors. But as I argued in my paper
[2] Free products of higher operad algebras
http://arxiv.org/abs/0909.4722
in which such a tensor product is defined for any structure definable by a "normalised higher operad" in the sense of Batanin, the name "free product" is a better choice of terminology.
Mark Weber
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2012-07-05 23:42 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
2012-07-04 14:10 Ondrej Rypacek
2012-07-05 13:38 ` Peter Selinger
2012-07-05 22:12 ` Ross Street
2012-07-05 23:42 ` Mark Weber [this message]
[not found] ` <EE7CBC13-DC4D-4ADD-ABB7-AA4E2D8E71B8@gmail.com>
2012-07-06 9:13 ` Ondrej Rypacek
2012-07-06 13:03 ` Omar Antolín Camarena
[not found] ` <1341579630.38166.YahooMailNeo@web110616.mail.gq1.yahoo.com>
2012-07-06 14:55 ` Ondrej Rypacek
2012-07-07 5:13 ` Vaughan Pratt
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