Completing triangulated categories

Henning Krause – 3 July 2019

The talk proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. This is a categorical analogue of the construction of the real numbers from the rationals via equivalence classes of Cauchy sequences, following Cantor and Meray. We apply this to categories of perfect complexes. For example, the bounded derived category of finitely presented modules over a right coherent ring is the completion of the category of perfect complexes.