Descent on 2-Fibrations and Strongly 2-Regular 2-Categories

Autor: Claudio Hermida
Rok vydání: 2004
Předmět:
Zdroj: Applied Categorical Structures. 12:427-459
ISSN: 0927-2852
DOI: 10.1023/b:apcs.0000049311.17100.da
Popis: We consider pseudo-descent in the context of 2-fibrations. A 2-category of descent data is associated to a 3-truncated simplicial object in the base 2-category. A morphism q in the base induces (via comma-objects and pullbacks) an internal category whose truncated simplicial nerve induces in turn the 2-category of descent data for q. When the 2-fibration admits direct images, we provide the analogous of the Beck–Benabou–Roubaud theorem, identifying the 2-category of descent data with that of pseudo-algebras for the pseudo-monad q *Σ q . We introduce a notion of strong 2-regularity for a 2-category R, so that its basic 2-fibration of internal fibrations c od:F ib(R)→R admits direct images. In this context, we show that essentially-surjective-on-objects morphisms, defined by a certain lax colimit, are of effective descent by means of a Beck-style pseudo-monadicity theorem.
Databáze: OpenAIRE