Category Theoretic Interpretation of Rings

Abstract

We enhance the category of rings and the category of idempotented rings to 2-categories. After doing this, we prove an equivalence of 1-categories and 2-categories between the category of rings and the category of small preadditive categories with one object and between the category of idempotented rings and the category of small preadditive categories with finitely many objects. Under these equivalences, we demonstrate some analogues between notions in category theory and ring theory.