Geodesic
Analytic functors and weak pullbacks
Theory and applications of categories, The Tholen Festschrift, Tome 21 (2008), pp. 191-209.

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

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.
Classification : 18A25, 18D10, 18B05
Keywords: analytic functor, weak limit, weak pullback 
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     title = {Analytic functors and weak pullbacks},
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J. Adamek; J. Velebil. Analytic functors and weak pullbacks. Theory and applications of categories, The Tholen Festschrift, Tome 21 (2008), pp. 191-209. http://geodesic.mathdoc.fr/item/TAC_2008_21_a10/