Algebraic structure for bicategory enriched categories Original Research Article

We define algebraic structure on a locally finitely presentable W-category for a locally finitely presentable bicategory W with a small set of objects. We further define the W-category of algebras for a given algebraic structure. Each algebraic structure gives rise to a finitary W-monad with the same W-category of algebras. Moreover, every finitary W-monad arises in this way from some algebraic structure; but that algebraic structure is not uniquely determined by the monad.