  In this note we introduce several instructive examples of bijections found
between several different combinatorially defined sequences of sets. Each
sequence has cardinalities given by the Catalan numbers. Our results answer
some questions posed by R. Stanley in the addendum to his textbook. We actually
discuss two types of bijection, one defined recursively and the other defined
in a more local, relative, fashion. It is interesting to compare the results of
the two.
