Does anyone know results about the existance of initial model (in Cat or other categories) of 2-sketch or V-sketch with indexed limits, and that of other equivalent (or more general) formulations (e.g. higher-dimensional sketch of Power and Wells)?

I think of results analogous to the existance of the (family of) initial model in Set of FL or FLS sketch. Any relevant informations and references are much welcome.

Thanks in advance. ... Hiroyuki Miyoshi ... EMAIL: miyoshi@slab.sfc.keio.ac.jp

i'll overly busy until the end of '93, but here's some thoughts. you can probably describe (e.g. see my thesis, summer '94) the modeling of your V-sketchs in appropriate V-cats as set models of an FL sketch, or, more humanely, of an essentially algebraic presentation. then the initial Herbrand model of that gives you an initial V-cat model. actually there is some fiddling about approximating pseudo maps by strict maps, e.g. approximating non locally finitely presentable cats by locally finitely presentable ones. e.g. see the Australians on flexible limits. also M. Makkai, here at McGill, has a view of sketches in which weak initial models are seen as injective hulls. bon soir, J. Otto ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++