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A unified framework for generalized multicategories

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G.S.H. Cruttwell and Michael A. Shulman

Notions of generalized multicategory have been defined in numerous
contexts throughout the literature, and include such diverse examples as
symmetric multicategories, globular operads, Lawvere theories, and
topological spaces. In each case, generalized multicategories are defined
as the ``lax algebras'' or ``Kleisli monoids'' relative to a ``monad'' on
a bicategory. However, the meanings of these words differ from author to
author, as do the specific bicategories considered. We propose a unified
framework: by working with monads on double categories and related
structures (rather than bicategories), one can define generalized
multicategories in a way that unifies all previous examples, while at the
same time simplifying and clarifying much of the theory.

Keywords:
Enriched categories, change of base, monoidal categories,
double categories, multicategories, operads, monads

2000 MSC:
18D05,18D20,18D50

*Theory and Applications of Categories,*
Vol. 24, 2010,
No. 21, pp 580-655.

http://www.tac.mta.ca/tac/volumes/24/21/24-21.dvi

http://www.tac.mta.ca/tac/volumes/24/21/24-21.ps

http://www.tac.mta.ca/tac/volumes/24/21/24-21.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/24/21/24-21.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/24/21/24-21.ps

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