The fundamental groupoid of a topological space 
is the groupoid
whose objects are the points of 
and whose morphisms are homotopy classes, relative to endpoints,
of paths in 
.
Composition is induced by path concatenation. The automorphism group of an object
is the fundamental group 
.
Fundamental Groupoid
See also
Fundamental Group, Groupoid, PathExplore with Wolfram|Alpha
References
Brown, R. Topology and Groupoids. Deganwy, Wales: BookSurge, 2006.Cite this as:
Weisstein, Eric W. "Fundamental Groupoid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FundamentalGroupoid.html