Anno, Rina and Logvinenko, Timothy
2021.
Bar category of modules and homotopy adjunction for tensor functors.
International Mathematics Research Notices
2021
(2)
10.1093/imrn/rnaa066
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Abstract
Given a DG-category A we introduce the bar category of modules Modbar(A). It is a DG-enhancement of the derived category D(A) of A which is isomorphic to the category of DG A-modules with A-infinity morphisms between them. However, it is defined intrinsically in the language of DG-categories and requires no complex machinery or sign conventions of A-infinity categories. We define for these bar categories Tensor and Hom bifunctors, dualisation functors, and a convolution of twisted complexes. The intended application is to working with DG-bimodules as enhancements of exact functors between triangulated categories. As a demonstration we develop homotopy adjunction theory for tensor functors between derived categories of DG-categories. It allows us to show in an enhanced setting that given a functor F with left and right adjoints L and R the functorial complex FR→FRFR→FR→Id lifts to a canonical twisted complex whose convolution is the square of the spherical twist of F. We then write down four induced functorial Postnikov towers computing this convolution.
Item Type: | Article |
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Date Type: | Publication |
Status: | Published |
Schools: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Publisher: | Oxford University Press |
ISSN: | 1073-7928 |
Date of First Compliant Deposit: | 3 March 2020 |
Date of Acceptance: | 3 March 2020 |
Last Modified: | 26 Jan 2021 17:45 |
URI: | http://orca.cf.ac.uk/id/eprint/130090 |
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