论文标题
fi $^m $的本地自注明属性
Locally Self-injective Property of FI$^m$
论文作者
论文摘要
在本文中，我们考虑了有限集和注射的类别的产品fi $^m $的本地自我注射属性。明确地，我们证明了外部张量产品与共同诱导函数的通勤，因此可以保留外观模块。作为冠状动物，在一个特征0的领域上，每个投射的fi $^m $模块都是含有的，而有限生成的fi $^m $ - 模块的类别是有限生成的Torsion fi $^m $ -Modules类别的类别。
In this paper we consider the locally self-injective property of the product FI$^m$ of the category FI of finite sets and injections. Explicitly, we prove that the external tensor product commutes with the coinduction functor, and hence preserves injective modules. As corollaries, every projective FI$^m$-modules over a field of characteristic 0 is injective, and the Serre quotient of the category of finitely generated FI$^m$-modules by the category of finitely generated torsion FI$^m$-modules is equivalent to the category of finite dimensional FI$^m$-modules.
