The following elementary facts about certain commutative diagrams, called "squares," are stated and proved in terms of abelian groups and their homomorphisms. However, they are valid for arbitrary abelian categories and can be proved also for them. This does not need to be shown, since every abelian category can be embedded into the category of abelian groups with preservation of exact sequences according to a result due to S. Lubkin (1). Proofs are often omitted or given only for one half of a theorem, the other half being dual to the first. Generalizations to a larger class of diagrams containing all finite commutative diagrams are possible.