Timeline for Groupoids vs. action groupoids
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 18, 2013 at 16:45 | comment | added | Mikhail Borovoi | @Mkouboi: I do not assume that there is a $\Gamma$-fixed point in $X$, and therefore $\Gamma$ does not act on the fibres $A(x,-)$ or $A(-,x)$ or $A(x,x)$. | |
| May 18, 2013 at 16:08 | comment | added | Mkouboi | @Mikhail: A groupoid isomorphism from $A\rightrightarrows X$ to $G\ltimes X\rightrightarrows X$ induces a $\Gamma$-action on the group bundle $G\ltimes X$. One obtains the $\Gamma$-action on $G$ by identifying $G$ with the fibres $(G\ltimes X)_x=(G\ltimes X)^x=(G\ltimes X)^x_x$. | |
| May 17, 2013 at 17:07 | comment | added | Mikhail Borovoi | @Mkouboi: I do not understand your answer. You write: "Moreover, any connected Γ-groupoid is in particular connected and hence in the form G⋉X. By construction of the group G, Γ acts compatibly on it and X..." But the construction of $G$ from the groupoid A⇉X is not functorial, so I do not understand how you get an action of Γ on G. Could you please add details? | |
| May 17, 2013 at 15:34 | history | answered | Mkouboi | CC BY-SA 3.0 |