Publication
Title
Tetramodules over a bialgebra form a 2-fold monoidal category
Author
Abstract
 Let B be an associative bialgebra over any field. A module over B in the sense of deformation theory is a tetramodule over B. All tetramodules form an abelian category. This category was studied by R. Taillefer (Algebr Represent Theory 7(5):471-490, 2004) and R. Taillefer (J Algebra 276(1):259-279, 2004). In particular, she proved that for any bialgebra B, the abelian category has enough injectives, and that Ext (a (TM) aEuro parts per thousand)(B,B) in this category coincides with the Gerstenhaber-Schack cohomology of B. We prove that the category of tetramodules over any bialgebra B is a 2-fold-monoidal category, with B a unit object in it. Roughly, this means that the category admits two monoidal structures, with common unit B, which are compatible in some rather non-trivial way (the concept of an n-fold monoidal category is introduced in Baltenu et al. (Adv Math 176:277-349, 2003)). Within (yet unproven) 2-fold monoidal analogue of the Deligne conjecture, our result would imply that RHom (a (TM) aEuro parts per thousand)(B,B) in the category of tetramodules is naturally a homotopy 3-algebra.
Language
English
Source (journal)
Applied categorical structures. - Dordrecht, 1993, currens
Publication
Dordrecht : 2013
ISSN
0927-2852
Volume/pages
21:3(2013), p. 291-309
ISI
000318286100004
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
 Faculty/Department Research group Publication type Subject Affiliation Publications with a UAntwerp address