The structure of double groupoids

NICOLÁS ANDRUSKIEWITSCH Y SONIA NATALE

JOURNAL OF PURE AND APPLIED ALGEBRA

Elsevier Science

Lugar: Amsterdam; Año: 2009 vol. 213 p. 1031 - 1045

0022-4049

We give a general description of the structure of a discrete double groupoid (with an extra, quite natural, filling condition) in terms of groupoid factorizations and groupoid 2-cocycles with coefficients in abelian group bundles. Our description goes as follows: To any double groupoid, we associate an abelian group bundle and a second double groupoid, its frame. The frame satisfies that every box is determined by its edges, and thus is called a `slim´ double groupoid. In a first step, we prove that every double groupoid is obtained as an extension of its associated abelian group bundle by its frame. In a second, independent, step we prove that every slim double groupoid with filling condition is completely determined by a factorization of a certain canonically defined `diagonal´ groupoid.