  We show that an abelian category can be exactly, fully faithfully embedded
into a module category as the right perpendicular subcategory to a set of
modules or module morphisms if and only if it is a locally presentable abelian
category with a projective generator, or in other words, the category of models
of an additive algebraic theory of possibly infinite bounded arity. This
includes the categories of contramodules over topological rings and other
examples. Various versions of the definition of the right perpendicular
subcategory are considered, all leading to the same class of abelian
categories. We also discuss sufficient conditions under which the natural
forgetful functors from the categories of contramodules to the related
categories of modules are fully faithful.
