THE CATEGORY OF L-ALGEBRAS

The category LAlg of L-algebras is shown to be complete and cocomplete, regular with a zero object and a projective generator, normal and subtractive, ideal determined, but not Barr-exact. Originating from algebraic logic, L-algebras arise in the theory of Garside groups, measure theory, functional analysis, and operator theory. It is shown that the category LAlg is far from protomodular, but it has natural semidirect products which have not been described in category-theoretic terms.