Doubling bialgebras of finite topologies

Mohamed Ayadi (1, 2) , Dominique Manchon (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 Département de Mathematiques [Sfax]

The species of finite topological spaces admits two graded bimonoid structures, recently defined by F. Fauvet, L. Foissy, and the second author. In this article, we define a doubling of this species in two different ways. We build a bimonoid structure on each of these species and describe a cointeraction between them. We also investigate two related associative products obtained by dualisation.

Mots clés: 2010 Mathematics Subject Classification. 16T05; 16T10; 16T15. 16T30; 06A11 Finite topological spaces; Species; Bimonoids; Bialgebras; Hopf algebras; Comodules

Domaines: Anneaux et algèbres [math.RA]

Mohamed Ayadi, Dominique Manchon. Doubling bialgebras of finite topologies. 2020. ⟨hal-03002352v2⟩