nLab well-powered abelian category

A locally small abelian category is an abelian category which is well-powered. In other words, (equivalent classes of) subobjects of any set form a set.

Remark. In older literature and occasionally in some contemporary literature in the subject of abelian categories locally small signifies what is now standardly called well-powered category. As every abelian category is a locally small category in the usual sense (all Homs are sets), the terminology locally small abelian category (if the modifier is understood as nontrivial) does not lead to ambiguities (hence it denotes a well-powered abelian category).