7 Sep
2001
7 Sep
'01
9:56 a.m.
A week or so ago, I asked the question about injectives in a category of modules in over a ring object in a Grothendieck topos. I asked whether if I is an injective module and E is an object of the topos, I^E is injective. I got no useful answers. Here is a related question. Does anyone know if an injective is interally injective? That is, if A and B are modules, then there is an object of the topos A -o B that is the subobject of B^A consisting of the additive morphisms. So what I am asking is whether for an injective I, the induced B -o I --> A -o I is epic. Or rather, can every module be embedded into an internal injective? Is there an internally injective cogenerator? Michael