  A non-unital algebra in a closed monoidal category is called self-induced if
the multiplication induces an isomorphism between A\otimes_A A and A. For such
an algebra, we define smoothening and roughening functors that retract the
category of modules onto two equivalent subcategories of smooth and rough
modules, respectively. These functors generalise previous constructions for
group representations on bornological vector spaces. We also study the pairs of
adjoint functors between categories of smooth and rough modules that are
induced by bimodules and Morita equivalence.
