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We give a definition of an operad with general groups of equivariancesuitable 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 inCat. We show that any operad is finitary, that an operad is cartesian if andonly if the group actions are nearly free (in a precise fashion), and that theexistence of a pseudo-commutative structure largely depends on the groups ofequivariance. We conclude by showing that the operad for strict braidedmonoidal categories has two canonical pseudo-commutative structures.

Operads with general groups of equivariance, and some 2-categorical aspects of operads in Cat