The coordinate projective line over a field is seen as a groupoid with a further `projection' structure. We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out of the geometry.
Keywords: projective geometry, groupoids, geometric algebra
2010 MSC: 18B40, 18D99, 51A25
Theory and Applications of Categories, Vol. 29, 2014, No. 13, pp 371-388.