Fundamental groupoid

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A groupoid (a category in which all morphisms are isomorphisms) defined from a topological space ; the objects are the points of , and the morphisms from an object to are the homotopy classes of paths starting at and ending at ; composition is the product of classes of paths. The group of automorphisms of an object is the same as the fundamental group .


A useful survey of the applications of fundamental groupoids can be found in [a1].


[a1] R. Brown, "From groups to groupoids: a brief survey" Bull. London Math. Soc. , 19 (1987) pp. 113–134
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Fundamental groupoid. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.V. Khokhlov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article