抽象范畴的连通性与特殊对象和特殊态射

讨论范畴的连通性与特殊对象和特殊态射的关系，主要结果有：（１）在连通范畴中，以始对象或终对象或零定义域（取值域）的态射皆为截片（保核收缩）、（２）在连通范畴中，任一始屿任一终对象必同主管（３）在范畴中，以始对象（终对象）为定义域（取值域）的态必为余常态射（常态射），（４）范Ｆ若遥零对象，则Ｆ一定是连通范畴，（５）若范畴中Ｆ中某一ｈｏｍｅ（Ａ，Ｂ）中至少有两个零态射，则Ａ一定不是连通范畴，更无零对象

THE RELATIONSHIP AMONG THE CONNECTEDNESS OF ABSTRACT CATEGORY AND SPECIAL OBJECTS AND SPECIAL MORPHISMS

In this paper, some relations among the connectedness of category, special objects and special morphisms are investigated. Some interesting new informations about them are obtained as following:(1)In a connected category, the morphisms whose domains (codomains) are initial objects, terminal objects or zero objects are all sections (retractions). (2)In a connected category, any initial object is isomorphic to any terminal object. (3)In a category, the morphisms whose domains are initial objects must be coconstant morphisms and the morphisms whose codomains are terminal objects must be constant morphisms. (4)If a category C has zero objects, then C must be a connected category. (5)If a hom C ( A,B ) of a category C has at least two zero morphisms, then the category C must not be a connected category, and C must not have any zero object.