Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

Bar category of modules and homotopy adjunction for tensor functors

Anno, Rina and Logvinenko, Timothy ORCID: 2021. Bar category of modules and homotopy adjunction for tensor functors. International Mathematics Research Notices 2021 (2) , pp. 1353-1462. 10.1093/imrn/rnaa066

[thumbnail of bar-category-of-modules-and-homotopy-adjunction-for-tensor-functors.pdf]
PDF - Accepted Post-Print Version
Download (797kB) | Preview


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
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: 07 Nov 2023 00:00

Citation Data

Cited 1 time in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item Edit Item


Downloads per month over past year

View more statistics