Relative Frobenius algebras are groupoids
  We functorially characterize groupoids as special dagger Frobenius algebras in the category of sets and relations. This is then generalized to a non-unital setting, by establishing an adjunction between H*-algebras in the category of sets and relations, and locally cancellative regular semigroupoids. Finally, we study a universal passage from the former setting to the latter. 
Chris Heunen, Ivan Contreras, Alberto S. Cattaneo
math.CT