sage: M = Manifold(2, 'R^2', structure='topological')
sage: c_cart.<x,y> = M.chart() # Cartesian coordinates on R^2
sage: c_cart.category()
Category of objects

sage: M = Manifold(2, 'R^2', structure='topological') 
sage: c_cart.<x,y> = M.chart() # Cartesian coordinates on R^2 
sage: c_cart.category() 
Category of elements of 
 Set of Morphisms 
  from 2-dimensional topological manifold R^2 
  to Vector space of dimension 2 over Real Field with 53 bits of precision 
  in Category of sets

sage: M = Manifold(2, 'M', field='complex', structure='topological') 
sage: X.<x,y> = M.chart(coord_restrictions=lambda x,y: [abs(x)<1, y!=0]) 
sage: X.codomain()                                                                                                                                                                                   
{ (x, y) ∈ Vector space of dimension 2 over Complex Field with 53 bits of precision : abs(x) < 1, y != 0 }