  We introduce a two-sorted algebraic theory whose models are states of
MV-algebras and, to within a categorical equivalence that extends Mundici's
well-known one, states of Abelian lattice-groups with (strong order) unit. We
discuss free states, and their relation to the universal state of
an~MV-algebra. We clarify the relationship of such universal states with the
theory of affine representations of lattice-groups. Main result: The universal
state of any locally finite MV-algebra---in particular, of any Boolean
algebra---has semisimple codomain.
