Antipodes of monoidal decomposition spaces

Louis Carlier, Joachim Kock

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Resum

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 originalEnglish
Número d’article1850081
RevistaCommunications in Contemporary Mathematics
Volum22
Número2
DOIs
Estat de la publicacióPublicada - 1 de març 2020

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