| Description |
1 online resource (v, 146 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 243, number 1151 |
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Memoirs of the American Mathematical Society ; no. 1151.
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| Contents |
Introduction -- Prerequisites -- Extension categories -- The Retakh isomorphism -- Hochschild cohomology -- A bracket for monoidal categories -- Application I: The kernel of the Gerstenhaber bracket -- Application II: The Ext-algebra of the identity functor -- Appendix A. Basics -- Bibliography |
| Summary |
In this monograph, we extend S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore we establish an explicit description of an isomorphism by A. Neeman and V. Retakh, which links 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, we show that our construction behaves well with respect to structure preserving functors between exact monoidal categories. We use our main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, we further determine a significant part of the Lie bracket's kernel, and thereby prove a conjecture by L. Menichi. Along the way, we introduce n-extension closed and entirely extension closed subcategories of abelian categories, and study some of their properties |
| Notes |
"Volume 243, number 1151 (fourth of 4 numbers), September 2016." |
| Bibliography |
Includes bibliographical references (pages 141-146) |
| Notes |
Online resource; title from PDF title page (viewed June 23, 2016) |
| Subject |
Homotopy theory.
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Geometry, Algebraic.
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Associative rings.
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Rings (Algebra)
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Associative rings
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Geometry, Algebraic
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Homotopy theory
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Rings (Algebra)
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| Form |
Electronic book
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| Author |
American Mathematical Society, publisher
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| LC no. |
2016037447 |
| ISBN |
9781470434502 |
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1470434504 |
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