  We give a definition of an operad with general groups of equivariance
suitable for use in any symmetric monoidal category with appropriate colimits.
We then apply this notion to study the 2-category of algebras over an operad in
Cat. We show that any operad is finitary, that an operad is cartesian if and
only if the group actions are nearly free (in a precise fashion), and that the
existence of a pseudo-commutative structure largely depends on the groups of
equivariance. We conclude by showing that the operad for strict braided
monoidal categories has two canonical pseudo-commutative structures.
