Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology. (Record no. 127906)
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| fixed length control field | 04521nam a22004813i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4901870 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131324.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2016 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470434502 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470419950 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4901870 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4901870 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)952109203 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA612.7 .H47 2016 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 514/.23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Hermann, Reiner. |
| 245 10 - TITLE STATEMENT | |
| Title | Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2016. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2016. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (158 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.243 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Introduction -- Background -- Main results -- Outline -- Conventions -- Chapter 1. Prerequisites -- 1.1. Exact categories -- 1.2. Monoidal categories -- 1.3. Examples: Exact and monoidal categories -- Chapter 2. Extension categories -- 2.1. Definition and properties -- 2.2. Homotopy groups -- 2.3. Lower homotopy groups of extension categories -- 2.4. -Extension closed subcategories -- Chapter 3. The Retakh isomorphism -- 3.1. An explicit description -- 3.2. Compatibility results -- 3.3. Extension categories for monoidal categories -- Chapter 4. Hochschild cohomology -- 4.1. Basic definitions -- 4.2. Gerstenhaber algebras -- Chapter 5. A bracket for monoidal categories -- 5.1. The Yoneda product -- 5.2. The bracket and its properties -- 5.3. The module case -Schwede's original construction -- 5.4. Morita equivalence -- 5.5. The monoidal category of bimodules -- Chapter 6. Application I: The kernel of the Gerstenhaber bracket -- 6.1. Introduction and motivation -- 6.2. Bialgebroids -- 6.3. A monoidal functor -- 6.4. Comparison to Linckelmann's result -- Chapter 7. Application II: The \Ext-algebra of the identity functor -- 7.1. The evaluation functor -- 7.2. Exact endofunctors -- 7.3. \Ext-algebras and adjoint functors -- 7.4. Hochschild cohomology for abelian categories -- Acknowledgements -- Appendix A. Basics -- A.1. Homological lemmas -- A.2. Algebras, coalgebras, bialgebras and Hopf algebras -- A.3. Examples: Hopf algebras -- Bibliography -- Main references -- Supplemental references -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | In 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. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Homotopy theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Geometry, Algebraic. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Associative rings. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Rings (Algebra). |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Hermann, Reiner |
| Title | Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2016 |
| International Standard Book Number | 9781470419950 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901870">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901870</a> |
| Public note | Click to View |
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