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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