(Answering Somnath Basu's question) Not really. My motivation is that I am trying to define a "categorically sound" definition of a "finitely related" algebra, i.e., one which is preserved under categorical equivalences. A first proposal would be the direct sum of a projective and a finitely presentable, but a better concept would be the retracts of those. I was curious to know when they are the same. Michel Hebert