The lifting property refers to the ability of certain modules, specifically projective modules, to 'lift' a map from a quotient module to the original module. In essence, if you have a surjective map from a module to another, and a homomorphism defined on the target module, the lifting property allows for the existence of a homomorphism that makes the diagram commute. This property connects projective modules to various important concepts in algebra, like exact sequences and free modules.
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