Category Rmod as abelian category

Let \(R\) be a ring and \(\mathrm{RMod}\) the category RMod. Then \(\mathrm{RMod}\) is an abelian category

1. zero object in RMod
2. Category RMod as bicomplete category
3. Homomorphiesatz für Moduln / abelian category and coimage isomorphic to image
4. Menge der Modulhomomorphismen als abelsche Gruppe