Fundamental groupoid
From Encyclopedia of Mathematics
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 
.
Comments
A useful survey of the applications of fundamental groupoids can be found in [a1].
References
| [a1] | R. Brown, "From groups to groupoids: a brief survey" Bull. London Math. Soc. , 19 (1987) pp. 113–134 |
How to Cite This Entry:
Fundamental groupoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fundamental_groupoid&oldid=35922
Fundamental groupoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fundamental_groupoid&oldid=35922
This article was adapted from an original article by A.V. Khokhlov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article