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Doubling bialgebras of finite topologies. (English) Zbl 1480.16059

The species of finite topological spaces admit a bimonoid structure together with a compatible internal coproduct, recently defined in [F. Fauvet et al., Ann. Inst. Fourier 67, No. 3, 911–945 (2017; Zbl 1431.16036)]. In the present paper, the authors define a doubling of this species.
The procedure of doubling has its origin in the Connes-Kreimer Hopf-algebraic interpretation of the Bogoliubov-Parasiuk-Hepp-Zimmermann renormalization procedure in the quantum field theory.

MSC:

16T05 Hopf algebras and their applications
16T10 Bialgebras
16T15 Coalgebras and comodules; corings
16T30 Connections of Hopf algebras with combinatorics
06A11 Algebraic aspects of posets

Citations:

Zbl 1431.16036
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References:

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