Antipodes of monoidal decomposition spaces

Louis Carlier, Joachim Kock

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Resumen

We introduce a notion of antipode for monoidal (complete) decomposition spaces, inducing a notion of weak antipode for their incidence bialgebras. In the connected case, this recovers the usual notion of antipode in Hopf algebras. In the non-connected case, it expresses an inversion principle of more limited scope, but still sufficient to compute the Möbius function as μ = ζ o S, just as in Hopf algebras. At the level of decomposition spaces, the weak antipode takes the form of a formal difference of linear endofunctors Seven-Sodd, and it is a refinement of the general Möbius inversion construction of Gálvez-Kock-Tonks, but exploiting the monoidal structure.

Idioma originalInglés
Número de artículo1850081
PublicaciónCommunications in Contemporary Mathematics
Volumen22
N.º2
DOI
EstadoPublicada - 1 mar 2020

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