Abstract :
We introduce a strengthening of the concept of purity, which may be more appropriate in the context of accessible categories (and which we prove to be equivalent to the usual one in locally presentable categories). We then use it to obtain a characterization of (cone) injectivity classes which, in particular, provides a solution to the corresponding problem of Fuchs (in the context of abelian groups) which avoids the set-theoretical assumptions of the Adámek-Rosický solution.
