A construction of 2-filtered bicolimits of categories
Eduardo J. Dubuc, Ross Street
备注：
This is a revision of arXiv:math/0605304 [math.CT]. It was pointed out to us by Martin Szyld that what was Lemma 1.14 could not be proved at that point. What was Lemma 1.20 depended on it. The old Definition 2.1 is replaced by new material. The old Lemma 1.14 can then be proved now as Lemma 2.6. The old Lemma 1.20 (with typos corrected) is now Lemma 2.7. A few minor typos were also corrected
发表信息：
Cahiers de topologie et géométrie différentielle catégoriques 47(2) (2006) 83--106
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. Kennison already considered 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 ours, but the other direction of this equivalence is not entirely trivial.
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