  We define lifting properties for universal algebras, which we study in this
general context and then particularize to various such properties in certain
classes of algebras. Next we focus on residuated lattices, in which we
investigate lifting properties for Boolean and idempotent elements modulo
arbitrary, as well as specific kinds of filters. We give topological
characterizations to the lifting property for Boolean elements and several
properties related to it, many of which we obtain by means of the reticulation.
