P-categorical equivalence of lattices

Recall that two algebras A and B are called categorically equivalent, if there is a categorical equivalence between the varieties they generate that maps A to B. We denote by A+ the algebra obtained from an algebra A by adding to its fundamental operations all nullary operations on A. We will call algebras A and B p-categorically equivalent if A+ and B+ are categorically equivalent. In the talk we will discuss p-categorical equivalence of lattices.