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Lax formal theory of monads, monoidal approach to bicategorical structures and generalized operads
Theory and applications of categories, Tome 30 (2015), pp. 332-386

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Generalized operads, also called generalized multicategories and $T$-monoids, are defined as monads within a Kleisli bicategory. With or without emphasizing their monoidal nature, generalized operads have been considered by numerous authors in different contexts, with examples including symmetric multicategories, topological spaces, globular operads and Lawvere theories. In this paper we study functoriality of the Kleisli construction, and correspondingly that of generalized operads. Motivated by this problem we develop a lax version of the formal theory of monads, and study its connection to bicategorical structures.

Publié le :
Classification : 18C15, 18D05, 18D50
Keywords: Bicategories, equipments, formal theory of monads, generalized multicategories, lax categorification, tricategories} 
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     author = {Dimitri Chikhladze},
     title = {Lax formal theory of monads, monoidal approach to bicategorical 
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     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a9/}
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Dimitri Chikhladze. Lax formal theory of monads, monoidal approach to bicategorical 
structures and generalized operads. Theory and applications of categories, Tome 30 (2015), pp. 332-386. http://geodesic.mathdoc.fr/item/TAC_2015_30_a9/