Concerning that the relation between Welsh′s weak maps and strong maps is not very good, a new definition of weak map is given and the concepts of rank-weak maps and independent sets-reflected maps are introduced. Thus a strong map must be weak and a map is rank-weak if and only if its extension is!weak. Then the relations among rank-weak maps, independent set-reflected maps and closed set-reflected are studied. The isomorphism between matroids is characterized by these new maps, which shows that both weak map and rank-weak map are appropriate morphisms for matroids.

matroid; rank function; weak map; rank-weak map