| 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) |
|
|
| | |
|