  Differential calculus on metric spaces is contained in the algebraic study of
normed groupoids with $\delta$-structures. Algebraic study of normed groups
endowed with dilatation structures is contained in the differential calculus on
metric spaces.
  Thus all algebraic properties of the small world of normed groups with
dilatation structures have equivalent formulations (of comparable complexity)
in the big world of metric spaces admitting a differential calculus.
  Moreover these results non trivially extend beyond metric spaces, by using
the language of groupoids.
