# The Stacks Project

## Tag: 01I2

This tag has label schemes-lemma-category-affine-schemes and it points to

The corresponding content:

Lemma 22.6.5. The category of affine schemes is equivalent to the opposite of the category of rings. The equivalence is given by the functor that associates to an affine scheme the global sections of its structure sheaf.

Proof. This is now clear from Definition 22.5.5 and Lemma 22.6.4. $\square$

\begin{lemma}
\label{lemma-category-affine-schemes}
The category of affine schemes is equivalent to the opposite of the
category of rings. The equivalence is given by the functor that associates
to an affine scheme the global sections of its structure sheaf.
\end{lemma}

\begin{proof}
This is now clear from Definition \ref{definition-affine-scheme}
and Lemma \ref{lemma-morphism-into-affine}.
\end{proof}


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