Abstract: 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 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.
ECS-LFCS-96-342, April 1996.
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