lax V-functors

lax V-functors

[Björn Gohla]

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

[Michael Shulman]

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?


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