Section MapMatrixSpaces.
Variables (aF rF : fieldType) (f : {rmorphism aF -> rF}).
Local Notation "A ^f" := (map_mx f A) : ring_scope.

Lemma map_col_base m n (A : 'M_(m, n)) :
(col_base A)^f = castmx (erefl m, mxrank_map A) (col_base A^f).