A 7-page paper entitled Filtered colimits in the effective topos can be downloaded from: http://www.math.uu.nl/people/jvoosten/effcolim.ps.gz Abstract: we are concerned with the problem whether there is a small full dense subcategory in the effective topos (which would give a nice embedding of Eff into a sheaf topos). Since this topos has enough projectives, we may assume that such a category consists of the \lambda-small projectives for some cardinal \lambda. Basically, there are two theorems: 1. For \lambda regular, uncountable: the \lambda -small projectives are dense, precisely if the constant objects functor \nabla :Sets --> Eff preserves \lambda-filtered colimits. 2. \nabla : Sets --> Eff does not preserve \omega _1-filtered colimits (hence, by 1., the countable projectives are not dense). Jaap van Oosten