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- W52209217 abstract "Suppose that $G$ is a groupoid acting on a small category $H$ in the sense of cite[Definition 4]{NOT} and $Htimes_alpha G$ is the resulting semi-direct product category (as in cite[Proposition 8]{NOT}). We show that there exists a subcategory $H_r subseteq H$ satisfying some nice property called ``regularity'' such that $H_r times_alpha G = Htimes_alpha G$. Moreover, we show that there exists a so-called ``quasi action'' (see Definition ref{quasi}) $beta$ of $G$ on $C^*(H_r)$ (where $C^*(H_r)$ is the semigroupoid $C^*$-algebra as defined in cite{EXE}) such that $C^*(H_rtimes_alpha G) = C^*(H_r)times_beta G$ (where the crossed product for $beta$ is as defined in Definition ref{cross})." @default.
- W52209217 created "2016-06-24" @default.
- W52209217 creator A5052907133 @default.
- W52209217 date "2007-10-18" @default.
- W52209217 modified "2023-09-27" @default.
- W52209217 title "$C^*-$crossed product of groupoid actions on categories" @default.
- W52209217 cites W1512658558 @default.
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- W52209217 hasPublicationYear "2007" @default.
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