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Descent for Monads

##
Pieter Hofstra and Federico De Marchi

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.

Keywords:
Descent theory, monads, globular sets

2000 MSC:
18C15, 18D10, 18D30

*Theory and Applications of Categories,*
Vol. 16, 2006,
No. 24, pp 668-699.

http://www.tac.mta.ca/tac/volumes/16/24/16-24.dvi

http://www.tac.mta.ca/tac/volumes/16/24/16-24.ps

http://www.tac.mta.ca/tac/volumes/16/24/16-24.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/24/16-24.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/16/24/16-24.ps

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