View source for Fundamental groupoid

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A [[groupoid]] (a category in which all morphisms are isomorphisms) defined from a topological space $X$; the objects are the points of $X$, and the morphisms from an object $x_0$ to $x_1$ are the homotopy classes $\mathrm{rel} \{0,1\}$ of paths starting at $x_0$ and ending at $x_1$; composition is the product of classes of paths. The group of automorphisms of an object $x_0$ is the same as the [[fundamental group]] $\pi_1(X,x_0)$.



====Comments====
A useful survey of the applications of fundamental groupoids can be found in [[#References|[a1]]].

====References====
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  R. Brown,   "From groups to groupoids: a brief survey"  ''Bull. London Math. Soc.'' , '''19'''  (1987)  pp. 113–134 {{ZBL|0612.20032}}</TD></TR>
</table>