A construction of 2-filtered bicolimits of categories

EDUARDO J. DUBUC, ROSS STREET

CAHIERS DE TOPOLOGIE ET GEOMETRIE DIFFERENTIELLE CATEGORIQUES

Lugar: Amiens, Francia.; Año: 2006 vol. XLVI p. 15 - 39

0008-0004

We define the notion of 2-filtered 2-category and give an explicit construction of the bicolimit of a category valued 2-functor. A category considered as a trivial 2-category is 2-filtered if and only if it is a filtered category, and our construction yields a category equivalent to the category resulting from the usual construction of filtered colimits of categories. Weaker axioms suffice for this construction, and we call the corresponding notion pre 2-filtered 2-category. The full set of axioms is necessary to prove that 2-filtered bicolimits have the properties corresponding to the essential properties of filtered bicolimits. In [3, see full paper] Kennison already considers filterness conditions on a 2-category under the name of bifiltered 2-category. It is easy to check that a bifiltered 2-category is 2-filtered, so our results apply to bifiltered 2-categories. Actually Kennison´s notion is equivalent to our´s, but the other direction of this equivalence is not entirely trivial.