Locally Self-Injective Property of FI m

We consider the locally self-injective property of the product Formula: see text of category Formula: see text 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 Formula: see text-module over a field of characteristic 0 is injective, and the Serre quotient of the category of finitely generated Formula: see text-modules by the category of finitely generated torsion Formula: see text-modules is equivalent to the category of finite-dimensional Formula: see text-modules.