Prolocalisations of homological categories

Abstract

A prolocalisation of an homological (resp. semi-abelian) category is a regular full re ective subcategory, whose re ection preserves short exact sequences. We study the closure operator and the torsion theory associated with such a situation. We pay special attention to the bered, the epire ective and the monore ective cases. We give examples in algebra, topos theory, functional analysis.