In this paper, we construct a direct limit functor from the category of Bratteli diagrams to the category of dimension groups and we prove that it is an equivalence of categories. The notion of a classification functor was introduced by Elliott in 2010 for classification of separable C*-algebras, which is a functor from a (complicated) category to another (concrete) functor reducing the verification of isomorphism of two objects in the first category to verification of isomorphism of their images in the second category. Using this notion, we obtain several classification functors between the categories of dimension groups, C*-algebras, and Cantor minimal systems, leading to functorial formulations and generalizations of results of Giordano, Putnam, and Skau.

Keywords: classification functor, dimension group, Bratteli diagram, C*-algebra, Cantor minimal system, orbit equivalence

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