* lax V-functors
@ 2010-05-24 11:52 Björn Gohla
2010-05-24 18:09 ` Michael Shulman
0 siblings, 1 reply; 2+ messages in thread
From: Björn Gohla @ 2010-05-24 11:52 UTC (permalink / raw)
To: categories
dear cocategorists,
given a monoidal 2-category V (i.e. \tensor is a 2-functor in each variable)
there is an obvious definition of lax V-functors, lax V-transformations and
modifications between V-categories (in the ordinary sense). has this been
studied anywhere?
--
cheers,
björn
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* Re: lax V-functors
2010-05-24 11:52 lax V-functors Björn Gohla
@ 2010-05-24 18:09 ` Michael Shulman
0 siblings, 0 replies; 2+ messages in thread
From: Michael Shulman @ 2010-05-24 18:09 UTC (permalink / raw)
To: Björn Gohla; +Cc: categories
Dear Björn,
In my recent preprint "Not every pseudoalgebra is equivalent to a
strict one" (arXiv:1005.1520), I had occasion to consider pseudo
V-categories, pseudo V-functors, and V-icons for such a V -- these
form the 2-category Ps-T-Alg for a suitable 2-monad on the 2-category
of V-enriched graphs. Obviously lax T-morphisms will similarly be lax
V-functors. I didn't have any need for general V-transformations or
modifications, and they don't fall as naturally out of the 2-monad
setup, but I agree that the definitions are easy to write down. I
would also be interested to hear who may have studied these notions in
general.
Best,
Mike
2010/5/24 Björn Gohla <b.gohla@gmx.de>:
> dear cocategorists,
>
> given a monoidal 2-category V (i.e. \tensor is a 2-functor in each variable)
> there is an obvious definition of lax V-functors, lax V-transformations and
> modifications between V-categories (in the ordinary sense). has this been
> studied anywhere?
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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