| Version 28 |
Version 27 |
| \begin{definition} \textbf{Groupoid categories}, or {\em categories of groupoids}, can be defined |
\begin{definition} \textbf{Groupoid categories}, or {\em categories of groupoids}, can be defined |
| simply by considering a groupoid as a category {$\mathsf{\G}_1$} with all invertible morphisms, and objects |
simply by considering a groupoid as a category {$\mathsf{\G}_1$} with all invertible morphisms, and objects |
| defined by the groupoid class or set of groupoid elements; then, the groupoid category, \textbf{$\mathsf{\G}_2$}, |
defined by the groupoid class or set of groupoid elements; then, the groupoid category, \textbf{$\mathsf{\G}_2$}, |
| is defined as the \emph{$2$-category} whose objects are \textbf{$\mathsf{\G}_1$} categories (groupoids), and whose morphisms are functors of \textbf{$\mathsf{\G}_1$} categories consistent with the definition of groupoid homomorphisms, or in the case of topological groupoids, consistent as well with topological groupoid |
is defined as the \emph{$2$-category} whose objects are \textbf{$\mathsf{\G}_1$} categories (groupoids), and whose morphisms are functors of \textbf{$\mathsf{\G}_1$} categories consistent with the definition of groupoid homomorphisms, or in the case of topological groupoids, consistent as well with topological groupoid |
| \PMlinkname{homeomorphisms}{Homeomorphism}. The 2-category of groupoids \textbf{$\mathsf{\G}_2$}, plays a central role in the generalised, categorical Galois theory involving fundamental groupoid functors. |
\PMlinkname{homeomorphisms}{Homeomorphism}. The 2-category of groupoids \textbf{$\mathsf{\G}_2$}, plays a central role in the generalised, categorical Galois theory involving fundamental groupoid functors. |
| \end{definition} |
\end{definition} |
