Geodesic
Descent for Monads
Theory and applications of categories, Tome 16 (2006), pp. 668-699.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

Motivated by a desire to gain a better understanding of the ``dimension-by-dimension'' decompositions of certain prominent monads in higher category theory, we investigate descent theory for endofunctors and monads. After setting up a basic framework of indexed monoidal categories, we describe a suitable subcategory of Cat over which we can view the assignment C |-> Mnd(C) as an indexed category; on this base category, there is a natural topology. Then we single out a class of monads which are well-behaved with respect to reindexing. The main result is now, that such monads form a stack. Using this, we can shed some light on the free strict $\omega$-category monad on globular sets and the free operad-with-contraction monad on the category of collections.
Classification : 18C15, 18D10, 18D30
Keywords: Descent theory, monads, globular sets 
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     author = {Pieter Hofstra and Federico De Marchi},
     title = {Descent for {Monads}},
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     volume = {16},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2006_16_a23/}
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Pieter Hofstra; Federico De Marchi. Descent for Monads. Theory and applications of categories, Tome 16 (2006), pp. 668-699. http://geodesic.mathdoc.fr/item/TAC_2006_16_a23/