Title 



Tetramodules over a bialgebra form a 2fold 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):471490, 2004) and R. Taillefer (J Algebra 276(1):259279, 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 GerstenhaberSchack cohomology of B. We prove that the category of tetramodules over any bialgebra B is a 2foldmonoidal 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 nontrivial way (the concept of an nfold monoidal category is introduced in Baltenu et al. (Adv Math 176:277349, 2003)). Within (yet unproven) 2fold 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 3algebra.   
Language 



English
 
Source (journal) 



Applied categorical structures.  Dordrecht, 1993, currens  
Publication 



Dordrecht : 2013
 
ISSN 



09272852
 
Volume/pages 



21:3(2013), p. 291309
 
ISI 



000318286100004
 
Full text (Publisher's DOI) 


  
Full text (publisher's version  intranet only) 


  
