Interacting Hopf algebras

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• 作者：Filippo Bonchi^a ; ^{filippo.bonchi@ens-lyon.fr" class="auth_mail" title="E-mail the corresponding author} ; Paweł Sobociński^b ; ^{ps@ecs.soton.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Fabio Zanasi^c ; ^{fzanasi@cs.ru.nl" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：221
• 期：1
• 页码：144-184
• 全文大小：1643 K

文摘

We introduce the theory 5754c7965f959" title="Click to view the MathML source">IH_R${\mathbb{IH}}_{\mathsf{R}}$ of interacting Hopf algebras, parametrised over a principal ideal domain R$\mathsf{R}$. The axioms of 5754c7965f959" title="Click to view the MathML source">IH_R${\mathbb{IH}}_{\mathsf{R}}$ are derived using Lack's approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid–comonoid pairs. This construction is instrumental in showing that 5754c7965f959" title="Click to view the MathML source">IH_R${\mathbb{IH}}_{\mathsf{R}}$ is isomorphic to the PROP of linear relations (i.e. subspaces) over the field of fractions of R$\mathsf{R}$.