We define exact sequences in the enchilada category of C*-algebras and correspondences, and prove that the reduced-crossed-product functor is not exact for the enchilada categories. Our motivation was to determine whether we can have a better understanding of the Baum-Connes conjecture by using enchilada categories. Along the way we prove numerous results showing that the enchilada category is rather strange.
Keywords: short exact sequence, C*-correspondence, exact functor, crossed product
2020 MSC: Primary 46L55; Secondary 18B99
Theory and Applications of Categories, Vol. 35, 2020, No. 12, pp 350-370.