On a generalized small-object argument for the injective subcategory problem
The structure of binary coproducts in the category of frames is analyzed, and the results are then applied widely in the study of compactness, local compactness (continuous frames), separatedness, pushouts and closed frame homomorphisms.
It is shown that the quotient maps of a monotopological construct A which are preserved by pullbacks along embeddings, projections, or arbitrary morphisms, can be characterized by being quotient maps in appropriate extensions of A.
In this paper we characterize weak monomorphisms and weak epimorphisms in the category of pro-groups. Also we define the notion of weakly exact sequence and we study this notion in the category of pro-groups.