Clubs

A club is a categorical gadget described by a monoid with respect to the substitution product. First invented by Kelly to formalize the “many-variable functorial calculus” used in defining monoidal categories, closed monoidal categories, and other doctrines of categories with extra structure, clubs are a generalization of symmetric operads and play a role in the development of “two-dimensional universal algebra” (2-monads and their algebras).