  We introduce the enriched notions of purity depending on the left class
$\mathcal E$ of a factorization system on the base $\mathcal V$ of enrichment.
The ordinary purity is given by the class of surjective mappings in the
category of sets. Under specific assumptions, covering enrichment over
quantale-valued metric spaces, $\omega$-complete posets, and quasivarieties, we
characterize the $(\lambda,\mathcal E)$-injectivity classes of locally
presentable $\mathcal V$-categories in terms of closure under a class of
limits, $\lambda$-filtered colimits, and $(\lambda,\mathcal E)$-pure
subobjects.
