Voir la notice de l'article provenant de la source Theory and Applications of Categories website
We define and study familial 2-functors primarily with a view to the development of the 2-categorical approach to operads of [Weber, 2005]. Also included in this paper is a result in which the well-known characterisation of a category as a simplicial set via the Segal condition, is generalised to a result about nice monads on cocomplete categories. Instances of this general result can be found in [Leinster, 2004], [Berger, 2002] and [Moerdijk-Weiss, 2007b]. Aspects of this general theory are then used to show that the composite 2-monads of [Weber, 2005] that describe symmetric and braided analogues of the $\omega$-operads of [Batanin, 1998], are cartesian 2-monads and their underlying endo-2-functor is familial. Intricately linked to the notion of familial 2-functor is the theory of fibrations in a finitely complete 2-category [Street, 1974] [Street, 1980], and those aspects of that theory that we require, that weren't discussed in [Weber, 2007], are reviewed here.
@article{TAC_2007_18_a21,
author = {Mark Weber},
title = {Familial 2-functors and parametric right adjoints},
journal = {Theory and applications of categories},
pages = {665--732},
publisher = {mathdoc},
volume = {18},
year = {2007},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2007_18_a21/}
}
Mark Weber. Familial 2-functors and parametric right adjoints. Theory and applications of categories, Tome 18 (2007), pp. 665-732. http://geodesic.mathdoc.fr/item/TAC_2007_18_a21/