  This note is an introduction to several generalizations of the dendroidal
sets of Moerdijk--Weiss. Dendroidal sets are presheaves on a category of rooted
trees, and here we consider indexing categories whose objects are other kinds
of graphs with loose ends. We examine the Segal condition for presheaves on
these graph categories, which is one way to identify those presheaves that are
a certain kind of generalized operad (for instance wheeled properad or modular
operad). Several free / forgetful adjunctions between different kinds of
generalized operads can be realized at the presheaf level using only the left
Kan extension / restriction adjunction along a functor of graph categories.
These considerations also have bearing on homotopy-coherent versions of
generalized operads, and we include some questions along these lines.
