Enrichment and representability for triangulated categories

Steen, J. and Stevenson, G. (2017) Enrichment and representability for triangulated categories. Documenta Mathematica, 22, pp. 1031-1062.

Abstract

Given a fixed tensor triangulated category S we consider triangulated categories T together with an S-enrichment which is compatible with the triangulated structure of T. It is shown that, in this setting, an enriched analogue of Brown representability holds when both S and T are compactly generated. A natural class of examples of such enriched triangulated categories are module categories over separable monoids in S. In this context we prove a version of the Eilenberg–Watts theorem for exact coproduct and copower preserving S-functors, i.e., we show that any such functor between the module categories of separable monoids in S is given by tensoring with a bimodule.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Stevenson, Dr Gregory
• Authors: Steen, J., and Stevenson, G.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Documenta Mathematica
• Publisher: Deutsche Mathematiker Vereinigung
• ISSN: 1431-0635
• ISSN (Online): 1431-0643
• Copyright Holders: Copyright © 2017 The Authors
• First Published: First published in Documenta Mathematica 22: 1031-1062
• Publisher Policy: Reproduced in accordance with the publisher copyright policy