Is there a finite abelian category?

To put this question off the unanswered-list:

The question got an answer on mathoverflow by Jeremy Rickard:

"Take the category of (at most) countable-dimensional vector spaces over your favourite field. Then take the quotient by the Serre subcategory of finite-dimensional vector spaces. (And take a skeletal subcategory so that it strictly has only two objects.)

Then this is an abelian category with only one non-zero object, whose endomorphism ring is the endomorphism ring of a countable-dimensional vector space, localized at the set of endomorphisms with finite-dimensional kernel and cokernel."