Submission date: 29 April 2015.

Abstract:

We construct a possibly non-commutative groupoid from the failure of 3-uniqueness of a strong type. The commutative groupoid constructed by John Goodrick and Alexei Kolesnikov lives in the center of the groupoid.

A certain automorphism group approximated by the vertex groups of the non-commutative groupoids is suggested as a “fundamental group” of the strong type.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 1504.07731: pdf, ps.