I am interested in the following question. Given any lccc (locally cartesian closed category) C can one find a full internally complete sub-category which is NOT reflective ? Of course, I mean subcategory in the fibrational sense ! The answer is well known in the case that the subcategory is SMALL ! Then by FAFT internal completeness is equivalent to reflectiveness. My guess is that for full subcategories of an lccc (in the fibrational sense) the property of having equalizers fibrewise being stable under reindexing is NOT equivalent to smallness ! But what I am lacking is a counterexample. I have tried the Freyd cover of 'w'-Set (the category of realizability sets) but unfortunately this construct- ion preserves those colimits I wanted to get rid of. I also would be quite satisfied with a counterexample in the non-fibred case. But I guess in the category of sets such a counterexample cannot be found. Thomas Streicher