  Definable subcategories may be extended along a ring homomorphism directly,
by using their defining conditions in the new module category, or by tensoring
up with the new ring. We investigate what is preserved and reflected by these
processes. On the way, we introduce the notion of being atomic with respect to
a bimodule - a refinement of the Mittag-Leffler condition. Particular attention
is given to the case where the ring homomorphism is an elementary embedding.
