Embed is a strongly monoidal functor.
Propagate structure proofs properly. Clean the house.
Use automatic lifting instead of manually defining a lifted addition operator.
Lift all useful structure of the base category to the Abelian Category instead of manually reimplementing it.
Function spaces are also objects in Ab.
Define the endomorphism ring of an abelian group. Give an example for (Z, +) with End(Z, +) ~ (Z, +, *)
Make use of injectivity of data families. Major simplifications. Dunno why I didn't succeed last time around...
Add Modules and Algebras.