* Rider to my response to Jean Benabou
@ 2003-08-21 2:13 Ross Street
0 siblings, 0 replies; only message in thread
From: Ross Street @ 2003-08-21 2:13 UTC (permalink / raw)
To: categories, jean benabou
Dear Jean
After seeing both Brian and Max in the last two days, I would like to
add two remarks to my last message.
1) Brian pointed out that you did not ask for your base V to be
closed which is assumed in his paper in SLNM137. However, this is
not really a restriction: just embed V in its presheaves with
convolution closed monoidal structure.
2) Max reminded me of his old result (not in the LaJolla Proceedings,
but known soon after) that a monoidal V-category is none other than a
monoidal category W with a "normal" monoidal functor W --> V.
(Normal here means that the unit is preserved.) I think this was
mentioned by Max somewhere in the literature but I cannot remember
where; possibly SLNM420. The good thing about it is that V-categories
enriched in the monoidal V-category W turn out to be mere
W-categories. An example is the monoidal category W = DGAb of chain
complexes of abelian groups; it can be regarded as a monoidal
additive category (that is, enriched in abelian groups V = Ab) or as
a mere monoidal category; categories enriched in the latter are
automatically additive.
Best wishes,
Ross
^ permalink raw reply [flat|nested] only message in thread
only message in thread, other threads:[~2003-08-21 2:13 UTC | newest]
Thread overview: (only message) (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2003-08-21 2:13 Rider to my response to Jean Benabou Ross Street
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).