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Homotopy Theory of Differential Graded Modules and Adjoints of Restriction of Scalars

Abbasirad, Mohammad Mahdi (2014) Homotopy Theory of Differential Graded Modules and Adjoints of Restriction of Scalars. PhD thesis, University of Sheffield.

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Abstract

This study constructs two different model structures called projective and injective model on the category of differential graded modules over a differential graded ring and also provides an explicit description of fibrant and cofibrant objects for these models. The constructions are based on the concept and properties of semi-projective and semi-injective modules and other kinds of projectivity and injectivity in the category of differential graded modules. Also an analysis of behavior of functors; restriction, extension and co-extension of scalars is given. Furthermore, some conditions under which an adjunction becomes a Quillen pair and a Quillen pair becomes a Quillen equivalence are described. Additionally, a relationship between restriction and co-extension for compact Lie groups is discovered.

Item Type: Thesis (PhD)
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Identification Number/EthosID: uk.bl.ethos.617185
Depositing User: Mr Mohammad Mahdi Abbasirad
Date Deposited: 23 Jul 2014 14:23
Last Modified: 03 Oct 2016 11:17
URI: http://etheses.whiterose.ac.uk/id/eprint/6568

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