关于半模上的Hom函子

On Hom functor over semimodules

在半模范畴中,获得了关于半模上的Hom函子的两个自然同构:HomR( i∈IMi,Us) i∈IHomR(Mi,Us),HomR(Us, i∈IMi) i∈IHomR(Us,Mi).进一步地,利用半模的性质,分别举例论证了:在一般情况下,当第一变量为无限直积或第二变量为无限直和时,这样的同构不存在.

In this paper,we get two natural isomorphisms in semimodule category by virtue of properties of direct product and direct sum in semimodule.For semimodules,it is observed that there exists an analogue to modules on Hom functors,though there are differences in semimodules and modules.