Enrichment and representability for triangulated categories

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

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Publisher's URL: https://www.math.uni-bielefeld.de/documenta/vol-22/30.html


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
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 (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

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