Dear Categorists - The following claim should be well-known (or false), but I don't know a reference: Let Gpd be the 2-category consisting of groupoids functors natural transformations and let 1Type be the 2-category consisting of homotopy 1-types continuous maps homotopy classes of homotopies where for present purposes "homotopy 1-types" means "CW complexes with vanishing higher homotopy groups regardless of the choice of basepoint". Claim: Gpd and 1Type are equivalent (or "biequivalent", in older terminology). In fact I bet there is an explicit pseudo-adjunction between them, with the "fundamental groupoid" 2-functor going one way and the "Eilenberg-Mac Lane space" 2-functor going the other way. Does anyone know for sure? Know a reference? Best, jb