| Abstrakt: |
We consider the locally self-injective property of the product FI m of 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 -module 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. [ABSTRACT FROM AUTHOR] |
