  This note recalls the representation of regular theories T in terms of
set-valued functors on models given by Makkai(1990), and explicitly states the
representation theorem for the classifying topos Set[T] in terms of filtered
colimit preserving functors which can be extrapolated from the results of that
paper. That representation of Set[T] is then compared with topological
representations in the style of Butz and Moerdijk(1998) by showing that for a
certain natural topology on the space of models, preserving filtered colimits
is the same thing as being `continuous' in the sense of being an equivariant
sheaf. By using a slight variation of the topology originally presented in op.
cit., we obtain from this comparison a representation of Set[T] in terms of a
topological category of models and homomorphisms, where the restricted
topological groupoid of models and isomorphisms classifies a different
(non-regular) theory.
