  We study a certain type of action of categories on categories and on operads.
Using the structure of the categories {\Delta} and {\Omega} governing category
and operad structures, respectively, we define categories which instead encode
the structure of a category acting on a category, or a category acting on an
operad. We prove that the former has the structure of an elegant Reedy
category, whereas the latter has the structure of a generalized Reedy category.
In particular, this approach gives a new way to regard group actions on
categories and on operads.
