Abelian right perpendicular subcategories in module categories

Understand

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.