|
|
|||
|
||||
OverviewIn this monograph, the author extends S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore the author establishes an explicit description of an isomorphism by A. Neeman and V. Retakh, which links $\mathrm{Ext}$-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid. As a main result, the author shows that his construction behaves well with respect to structure preserving functors between exact monoidal categories. The author uses his main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, he further determines a significant part of the Lie bracket's kernel, and thereby proves a conjecture by L. Menichi. Along the way, the author introduces $n$-extension closed and entirely extension closed subcategories of abelian categories, and studies some of their properties. Full Product DetailsAuthor: Reiner HermannPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.241kg ISBN: 9781470419950ISBN 10: 1470419955 Pages: 146 Publication Date: 30 September 2016 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsIntroduction Prerequisites Extension categories The Retakh isomorphism Hochschild cohomology A bracket for monoidal categories Application I: The kernel of the Gerstenhaber bracket Application II: The $\mathbf{Ext}$-algebra of the identity functor Appendix A. Basics Bibliography.ReviewsAuthor InformationReiner Hermann, Norwegian University of Science and Technology, Trondheim, Norway. Tab Content 6Author Website:Countries AvailableAll regions |