Affine spaces over a give field are easily seen to be algebras of a particular equational theory. Hence the answer to Allen Knutsun's question: Is there a general theory on how to give representing objects additional structure, when one is interested in functors to other categories than Set? In the case I'm dealing with in particular, the terminal category has as objects affine spaces. can be found in the ancient work: Algebra-valued functors in general and tensor products in particular, Colloquium Mathematicum, XIV, 1966. ++++++++++++++++++++++++++++++++++++++++++++++++++