LDR 02881     2200349   4500
010    _a9781470419950
       _bbr.
011    _a0065-9266
090    _a16942
101    _aeng
102    _aUS
100    _a20150209              frey50       
200    _aMonoidal categories and the Gerstenhaber bracket in Hochschild cohomology
       _bM
       _fReiner Hermann
210    _aProvidence (R.I.)
       _cAmerican Mathematical Society
       _d2016
215    _a1 vol. (V-146 p.)
       _d26
       _cill.
225    _9170211
       _aMemoirs of the American Mathematical Society
       _v1151
       _x0065-9266
320    _aBibliogr. p. [141]-146. Index
330    _aIn 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
410    _9170209
       _aAMS
       _tMemoirs of the American Mathematical Society
       _x0065-9266
676    _a2010
686    _20
       _9162212
       _a16E40
       _bAssociative rings and algebras -- Homological methods
       _x(Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
686    _20
       _9162284
       _a16T05
       _bAssociative rings and algebras -- Hopf algebras, quantum groups and related topics
       _xHopf algebras and their applications
686    _20
       _9162440
       _a18D10
       _bCategory theory; homological algebra -- Categories with structure
       _xMonoidal categories, symmetric monoidal categories, braided categories
686    _20
       _9162450
       _a18E10
       _bCategory theory; homological algebra -- Abelian categories
       _xExact categories, abelian categories
686    _20
       _9162469
       _a18G15
       _bCategory theory; homological algebra -- Homological algebra
       _xExt and Tor, generalizations, Künneth formula
700    _4070
       _aHermann
       _bReiner
       _9183264
856    _uhttps://zbmath.org/?q=an%3A06786968
       _zzbMath
856    _uhttps://mathscinet.ams.org/mathscinet-getitem?mr=3518219
       _zMSN
856    _uhttp://www.ams.org/books/memo/1151/
       _zAMS-résumé
905    _aaw
       _b2018
906    _aaw
       _b2018-09-25
001     16942
995    _f12521-01
       _xachat Ebsco
       _918681
       _cCMI
       _20
       _kSéries AMS
       _o0
       _eCouloir
       _z84.36
       _bCMI
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