Dual Ramsey properties for classes of algebras

Almost any reasonable class of finite relational structures has the Ramsey property or a precompact expansion. In contrast to that, list classes algebras with expansion is surprisingly short. this paper we show that nontrivial variety (that is, equationally defined algebras) enjoys various dual properties. We develop completely new set strategies rely on fact left adjoints preserve property, and then treat as Eilenberg–Moore categories for monad. in have small degrees, every algebra big degree free countably many generators. As usual, these come consequences ordered versions statements.