There was a little but crucial mistake in my mail yesterday. The functors corresponding to generalized triposes over SS preserves finite limits and have bound 1. Implicit in Andy Pitts Thesis (1981) there is a geometric account of a mild generalisation of triposes. They are equivalent to finite limit preserving functors F : SS -> EE between toposes for which 1 is a bound, i.e. every object A of EE appears as subquotient of some FI. In lack of a better name I call these functors "weakly localic". My question is whether weakly localic maps are closed under composition? I guess that not but lack an example. If anyone had a suggestion I'd be very grateful! Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]