From: Fernando Muro <fmuro@us.es>
To: categories@mta.ca
Subject: reference on enriched monoidal categories
Date: Wed, 12 Jan 2011 08:50:03 +0100 [thread overview]
Message-ID: <E1PdBn0-0005b9-Pn@mlist.mta.ca> (raw)
Dear colleagues,
I'm looking for a reference where the following fact (that I believe to
be clearly true) is discussed:
Let V and C be biclosed monoidal categories. Suppose that V is symmetric
and that we have a strong braided monoidal functor z : V --> Z(C) to the
center of C in the sense of Joyal-Street. Assume further that the
functor z(-) \otimes Y : V --> C has a right adjoint Hom(Y,-) : C --> V
for any object Y in C. Then C is a monoidal V-category with Hom objects
in V given by this right adjoint.
You may assume that V and C are (co)complete if you wish.
It is easy to construct compositions morphisms, etc. in an elementary
way, but verifying all laws is a pain. This is why I'm willing to find a
reference.
All the best for the new year,
Fernando Muro
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2011-01-12 7:50 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-01-12 7:50 Fernando Muro [this message]
2011-01-14 0:55 ` Richard Garner
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=E1PdBn0-0005b9-Pn@mlist.mta.ca \
--to=fmuro@us.es \
--cc=categories@mta.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).