11. We thus take the Lie algebroid " A?! M " of the Poisson groupoid . 12. The point is that a disjoint union of groups is not a group but it is a groupoid . 13. Higgins has given a nice version of the normal form using the fundamental groupoid of a graph of groups. 14. As a more explicit example consider the Lie algebroid associated to the pair groupoid G : = M \ times M. 15. The symmetries of the fifteen puzzle form a groupoid ( not a group, as not all moves can be composed ). 16. I believe he explains both the group and groupoid ideas . talk ) 00 : 29, 3 November 2008 ( UTC) 17. Thus one has the "'fundamental groupoid "'instead of the fundamental group, and this construction is functorial. 18. Several groupoid and double groupoid representations ) and ^ tefan Odobleja; the latter is also regarded as the ideological father behind cybernetics. 19. Several groupoid and double groupoid representations ) and ^ tefan Odobleja; the latter is also regarded as the ideological father behind cybernetics. 20. In analogy, an action of a groupoid is a functor from the groupoid to the category of sets or to some other category.
