Can you tell me, where I can find a proof of the following fact: Let $R$ be a commutative ring. Consider the category of commutative Hopf algebras over $R$. Then this category is equivalent to the category of corepresentable functors from the category commutative $R$-algebras to groups.



Category of Hopf algebras.
I believe the argument you are looking for may be contained in Jens Carsten Jantzen's book *Representations of Algebraic Groups*, Part I, Sections 1.3 and 2.3. You may also wish to consult Chapter 1 of William C. Waterhouse's *Introduction to Affine Group Schemes*.


