000			04521nam a22004813i 4500
001			EBC4901870
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005			20240729131324.0
006			m o d |
007			cr cnu||||||||
008			240724s2016 xx o ||||0 eng d
020			_a9781470434502 _q(electronic bk.)
020			_z9781470419950
035			_a(MiAaPQ)EBC4901870
035			_a(Au-PeEL)EBL4901870
035			_a(OCoLC)952109203
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA612.7 .H47 2016
082	0		_a514/.23
100	1		_aHermann, Reiner.
245	1	0	_aMonoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2016.
264		4	_c©2016.
300			_a1 online resource (158 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.243
505	0		_aCover -- 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			_aIn 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			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic 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	_aHomotopy theory.
650		0	_aGeometry, Algebraic.
650		0	_aAssociative rings.
650		0	_aRings (Algebra).
655		4	_aElectronic books.
776	0	8	_iPrint version: _aHermann, Reiner _tMonoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology _dProvidence : American Mathematical Society,c2016 _z9781470419950
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901870 _zClick to View
999			_c127906 _d127906