A集的局部化

THE LOCALIZATION OF A-SETS

本文在 A 集范畴 Ens-A 中引入局部化的概念.证明了如果 A 集 M 是内射(右投射、平坦),则其局部化后得到 S^(-1) A 集 S^(-1) M 也是内射(右投射、平坦),并由此推出如果交换幺半群 A 是完全内射(完全投射,绝对平坦)的.则半群局部化 S^(-1) A 亦分别具有上述性质.同时本文证明了对于 A 集 M 和 N,及 A 的子半群 S(S 满足条件:■_(S1,S2) ∈S,存在■ y ∈A,使得 ys_1=ys_2 ∈S)有 S^(-1) A 同构:S^(-1) (M■ N)≌S^(-1) M■S^(-1) N.

In this paper we introduce the concept of localization in the category Ens-A of A-sets and prove that if an A- set M is right injective(right projective,flat),then the localization of M is a right injective(right projective,flat) S^(-1) A-set;and then we prove that if a monoid A is completely injective(projective),absolutely flat,then so is the localization S^(-1) A.At the end of the paper we discusse the relationship between the localization and tensor product of A-sets.