Joint work with Jiri Rosicky, Brno.

Lawvere introduced the idea to consider as equations expressions t=t' where t,t' are natural transformations U^n-->U, U being the forgetful functor U:Alg-->Set. This idea is dualised to coalgebras, and differences and analogies to the algebraic case are dicussed. In particular, we show the analog of Reiterman's theorem which characterises equationally definable classes in the absence of free algebras (equationally in the sense mentioned above).