We show that every action operad gives rise to a notion of monoidal category
via the categorical version of the Borel construction, embedding action operads
into the category of 2-monads on
. We characterize those 2-monads
in the image of this embedding, and as an example show that the theory of
coboundary categories corresponds precisely to the operad of
n-fruit cactus
groups. We
... [Show full abstract] finally define -multicategories for an action
operad , and show that they arise as monads in a Kleisli
bicategory.