Categories of relational structures

There is a book devoted to these questions: A.Pultr and V.Trnkova, Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North Holland 1980. The question whether complete lattices, etc. can be embedded into Str_n depends on what one means under embedd. If it is a full embedding, the problem is set-theoretical. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++