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
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 |
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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 |
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