Extending localization functors Original Research Article

We prove that, under suitable restrictions, an idempotent monad t defined on a full subcategory image of a category image can be extended to an idempotent monad T on image in a universal (terminal) way. Our result applies in particular to the case when t is P-localization of nilpotent groups (where P denotes a set of primes) and image is the category of all groups. The corresponding monad T on image is, in a certain precise sense, the best idempotent approximation to the usual Zp-completion of groups; it turns out to be a strict epimorphic image of Bousfieldʹs HZp-localization.