弱加法范畴

以可换么半群范畴心和半模范畴sM为背景建立了弱加法范畴的概念，讨论了弱加法范畴中有限个对象上积的性质，给出了保持有限对象上积的函子的等价刻划，进而定义了弱加法范畴的理想和同余关系，以此建立了弱加法范畴的商和同态基本定理及第一、二同构定理，并讨论了同余的格和亚直积等，以上概念和结果是对加法范畴的实质性拓广，为探讨弱加法范畴的结构奠定了必要的基础．

Weak Additive Category

In this paper, we introduce the concept of a weak additive category based on the category Abs of commutative monoids and the one sM of semimodules and discuss some properties of the coproducts of finite objects in it. Two necssary and sufficient conditions of that a functor of the category to itself reserves finite coproducts are given. Further, we introduce foe concepts of ideals, congruences of a weak additive category and, based on them, prove the fundamental theorem of homomorphisms of a weak additive category and the first (second) isomorphism theorem. Finally, we also discuss the lattice of congruences and subdirect products of weak additive categories. These concepts and results generalized that of additive categories and made a base of researches on the contructure of weak additive categories.