Mathematics – Category Theory
Scientific paper
2006-05-11
Mathematics
Category Theory
24 pages, many 2-cell diagrams, french abstract
Scientific paper
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 considers filterness conditions on a2-category under the name of bifiltered 2-category (see reference in paper). It is easy to check that a bifiltered 2-category is 2-filtered, so ourresults 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.
Dubuc Eduardo J.
Street Ross
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