  We provide several crucial technical extensions of the theory of stable
independence notions in accessible categories. In particular, we describe
circumstances under which a stable independence notion can be transferred from
a subcategory to a category as a whole, and examine a number of applications to
categories of groups and modules, extending results of [MAa]. We prove, too,
that under the hypotheses of [LRV], a stable independence notion immediately
yields higher-dimensional independence as in [SV].
