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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.

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Do you mean commutative Hopf algebras? –  Bruce Westbury Jun 28 '12 at 14:02
    
Yes, I mean commutative. Thanks for the hint, I have edited it. –  philipp Jun 28 '12 at 15:24

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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.

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