全序群范畴的Hom函子

A HOM-FUNCTOR FOR CATEGORY OF TOTALLY ORDERED GROUPS

设 A 是 Abelian 格序群,B 是 Abelian 全序群,本文证明了 Hom(A,B)是 Abelian 全序群,Hom(A,·)是 Abelian 全序群及其保序同态的范畴(?)到自身的共变函子,同时在全序模及其保序同态的范畴上得到了类似的结果.

Suppose A is an Abelian lattice ordered group and B is an Abelian totally ordered group.In the paper,the author shows that Hom(A,B) is an Abelian totally ordered group and Hom(A,·) is a covariant functor from the category of Abelian totally ordered groups and preserving homomorphisms into itself.Meanwhile,the author gets the similar results on the category of totally ordered modules and ordered preserving homomorphisms.