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Analytic functors and weak pullbacks

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J. Adamek and J. Velebil

For accessible set-valued functors it is well known that weak preservation
of limits is equivalent to representability, and weak preservation of
connected limits to familial representability. In contrast, preservation
of weak wide pullbacks is equivalent to being a coproduct of quotients of
$\hom$-functors modulo groups of automorphisms. For finitary functors this
was proved by Andr\'e Joyal who called these functors analytic. We
introduce a generalization of Joyal's concept from endofunctors of
**Set** to endofunctors of a symmetric monoidal category.

Keywords:
analytic functor, weak limit, weak pullback

2000 MSC:
18A25, 18D10, 18B05

*Theory and Applications of Categories,*
Vol. 21, 2008,
No. 11, pp 191-209.

http://www.tac.mta.ca/tac/volumes/21/11/21-11.dvi

http://www.tac.mta.ca/tac/volumes/21/11/21-11.ps

http://www.tac.mta.ca/tac/volumes/21/11/21-11.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/21/11/21-11.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/21/11/21-11.ps

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