M T W T F S S
 
 
1
 
2
 
3
 
4
 
5
 
6
 
7
 
8
 
9
 
10
 
11
 
12
 
13
 
14
 
15
 
16
 
17
 
18
 
19
 
20
 
21
 
22
 
23
 
24
 
25
 
26
 
27
 
28
 
29
 
30
 
31
 
 
 
Add to My Calendar

Responsabili:

Federica Galluzzi  ed  Elena Martinengo
 

Nel calendario si indicano i seminari di geometria algebrica e altre attività di interesse, organizzate dall'Università e dal Politecnico di Torino.

Evento

Titolo: Bihom bialgebras viewed as bimonoids (RIMANDATO A DATA DA DESTINARSI)
Dove: Palazzo Campana - TORINO
Relatore: Gabriella Bohm
Afferenza: Wigner Research Centre for Physics, Budapest, Ungheria.
Locandina: Locandina

Descrizione:

Abstract :Bihom bialgebras viewed as bimonoids

In recent years, lead by diverse motivations, several different generalizations of Hopf algebra have been proposed. Their similar features naturally raise the question whether they are instances of the same, more general notion. In [2,3] several examples, such as groupoids, Hopf monoids in braided monoidal categories, Hopf algebroids over central base algebras, weak Hopf algebras, Turaev’s Hopf group algebras, Batista-Caenepeel-Vercruysse’s Hopf categories and Bruguiéres’ Hopf polyads were unified as Hopf monoids in suitable duoidal (called 2-monoidal in [1]) categories.

BiHom-bimonoids in [5] however, do not seem to fit this picture. In order to find a framework describing them, we introduce monoidal categories whose monoidal products of any posiitive number of factors are lax coherent and whose nullary products are oplax coherent. We call them Lax+Oplax0-monoidal. Dually, we consider Lax0Oplax+-monoidal categories which are oplax coherent for positive numbers of factors and lax coherent for nullary monoidal products. We define LaxOplax0+ -duoidal categories with compatible Lax+Oplax0- and Lax0Oplax+-monoidal structures. We introduce comonoids in Lax+Oplax0-monoidal categories, monoids in Lax0Oplax+-monoidal categories and bimonoids in Lax+ 0Oplax0 + -duoidal categories.

The unital BiHom-monoids, counital BiHom-comonoids, and unital and counital BiHom-bimonoids of [5] are identified with the monoids, comonoids and bimonoids in a suitable Lax+ 0Oplax0+ -duoidal category, constructed by a method generalized from [4].

This is a joint work with Joost Vercruysse at ULB, Brussels.

 

[1]  Marcelo Aguiar and Swapneel Mahajan, Monoidal functors, species and Hopf algebras, volume 29 of CRM Monograph Series. American Mathematical Society, Providence, RI, 2010. 1, 2

[2]  Gabriella Böhm, Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads, Theor. and Appl. of Categories 32 no. 37 (2017) 1229–1257. 1

[3]  Gabriella Böhm and Stephen Lack, Hopf comonads on naturally Frobenius map-monoidales, J. Pure Appl. Algebra 220 no. 6 (2016) 2177–2213. 1

[4]  Stefaan Caenepeel and Isar Goyvaerts, Monoidal Hom-Hopf algebras, Comm. Algebra 39 (2011) 2216–2240.

[5]  Giacomo Grazianu, Abdenacer Makhlouf, Claudia Menini and Florin Panaite, BiHom- Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras, SIGMA 11 (2015), 086, 34 pages.

Sede

Sede: Palazzo Campana - Sito web
Indirizzo: Via Carlo Alberto 10
CAP: 10123
Città: TORINO