  We generalise the notion of separable equivalence, originally presented by
Linckelmann (2011), to an equivalence relation on additive categories. We use
this generalisation to show that from an initial equivalence between two
algebras we may build equivalences between many related categories. We also
show that separable equivalence preserves the representation type of an
algebra. This generalises Linckelmann's result, where he showed this in the
case of symmetric algebras. We use these theorems to show that the group
algebras of several small cyclic groups cannot be separably equivalent. This
gives several examples of algebras that have the same complexity but are not
separably equivalent.
