  This paper presents an in-reachability based classification of invariant
synchrony patterns in Coupled Cell Networks (CCNs). These patterns are encoded
through partitions on the set of cells, whose subsets of synchronized cells are
called colors. We study the influence of the structure of the network in the
qualitative behavior of invariant synchrony sets, in particular, with respect
to the different types of (cumulative) in-neighborhoods and the in-reachability
sets. This motivates the proposed approach to classify the partitions into the
categories of strong, rooted and weak, according to how their colors are
related with respect to the connectivity structure of the network. Furthermore,
we show how this classification system acts under the partition join ($ \vee $)
operation, which gives us the synchrony pattern that corresponds to the
intersection of synchrony sets.
