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We define lifting properties for universal algebras, which we study in thisgeneral context and then particularize to various such properties in certainclasses of algebras. Next we focus on residuated lattices, in which weinvestigate lifting properties for Boolean and idempotent elements moduloarbitrary, as well as specific kinds of filters. We give topologicalcharacterizations to the lifting property for Boolean elements and severalproperties related to it, many of which we obtain by means of the reticulation.

Algebraic and Topological Results on Lifting Properties in Residuated Lattices