categories - Category Theory list
 help / color / mirror / Atom feed
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/ ]


  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

Reply instructions:

You may reply publicly to this message via plain-text email
using any one of the following methods:

* Save the following mbox file, import it into your mail client,
  and reply-to-all from there: mbox

  Avoid top-posting and favor interleaved quoting:
  https://en.wikipedia.org/wiki/Posting_style#Interleaved_style

* Reply using the --to, --cc, and --in-reply-to
  switches of git-send-email(1):

  git send-email \
    --in-reply-to=E1Sn7pD-0004rg-CV@mlist.mta.ca \
    --to=mark.weber.math@googlemail.com \
    --cc=categories@mta.ca \
    --cc=ondrej.rypacek@gmail.com \
    --cc=selinger@mathstat.dal.ca \
    /path/to/YOUR_REPLY

  https://kernel.org/pub/software/scm/git/docs/git-send-email.html

* If your mail client supports setting the In-Reply-To header
  via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).