ON CERTAIN REFLECTIONS IN TOPOLOGICAL ALGEBRAIC SITUATIONS

Consider the following commutative square of-categories and functors where T and U are (regular epi. monosource) topological and fibre small. G is algebraic and the following two conditions hold: (i) if h: $UA{\rightarrow}UB$ and g: $VA{\rightarrow}VB$ are morphisms such that Gh=Tg. there exists a morphism f: $A{\rightarrow}B$ such that Uf=h and Vf=g; (ii) U-initial monosources are carried into T-initial monosources by V.