Abstract
I will finally get to some of the hard work and show, if time permits,
the following two results:
1. Assuming that V is the subobject and product closure of a very nice category S of topological objects and that S contains a very nice injective K, then K is also injective in V.
2. The inclusion of the weak objects in V has a left adjoint and the inclusion of the strong objects has a right adjoint.