The relationship between the category of all simple matroids with strong maps and the category of all matroids with strong maps are discussed. It is proved that the simplification of any matroid is isomorphic to the quotient matroid of this matroid under the parallel or equal relation.The left adjoint functor of the inclusion functor from the full subcategory of all simple matroids to the category of all matroids is constructed, which shows that the category of all simple matroids is a reflective subcategory of the category of all matroids.

simple matroid; quotient matroid; simplification of matroid; strong map; reflective subcategory.