This paper study the problem for the chaxacteriztions of the minus partial order ofmorphism set in a category, its main results are: 1. prove fourteen characterizations of the minuspartial order in a general category ; 2. the results that using inclusion relation of (1)-inverse,(1,2)-inverse and parallel sum characterized the minus partial order of a complex matrix by category; 3.give the inverse example for proposition 1(ix) of [5], then negate the Hartwig's this characterization.