The authors 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 the construction yields a category equivalent to the category resulting from the usual construction of filtered colimits of categories. Weaker axioms suffice, and the corresponding notion is called a 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.
|Number of pages||24|
|Journal||Cahiers de topologie et géométrie différentielle catégoriques|
|Publication status||Published - 2006|