ALGEBRAIC STRUCTURE FOR BICATEGORY ENRICHED CATEGORIES

We define algebraic structure on a locally finitely presentable W-cate gory for a locally finitely presentable bicategory W with a small set of objects. We further define the W-category of algebras for a given a lgebraic structure. Each algebraic structure gives rise to a finitary W-monad with the same W-category of algebras. Moreover, every finitary WS-monad arises in this way from some algebraic structure; but that a lgebraic structure is not uniquely determined by the monad. (C) 1998 E lsevier Science B.V. All rights reserved.