$\mathfrak {F}$-projective objects

Abstract:

Previously, projective abelian topological groups were defined based upon the requirement that free abelian topological groups be projective. In the present paper it is observed that a similar definition of projective relative to a functor which has a right adjoint leads to equivalent results in a much more general setting. These results are then specialized to the category of topological groups (with Markov’s free functor) for a detailed example.