do weakly localic maps of toposes compose?

Implicit in Andy Pitts Thesis (1981) there is a geometric account of a mild generalisation of triposes. They are equivalent to 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/ ]