replace more hacks

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Maximilian Keßler 2022-02-16 02:13:49 +01:00
parent 59fbfbb774
commit e0735ee92b

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@ -2630,7 +2630,7 @@ The following is somewhat harder than in the affine case:
\end{proof}
\begin{remark}
Note that giving a contravariant functor $\cC \to \cD$ is equivalent to giving a functor $\cC \to \cD\op$. We have thus shown that the category of affine varieties is equivalent to $\mathcal{A}\op$, where $\mathcal{A} \subsetneq \Alg_\mathfrak{k}$ is the full subcategory of $\mathfrak{k}$-algebras $A$ of finite type with $\nil(A) = \{0\}$.
Note that giving a contravariant functor $\mathcal{C} \to \mathcal{D}$ is equivalent to giving a functor $\mathcal{C} \to \mathcal{D}\op$. We have thus shown that the category of affine varieties is equivalent to $\mathcal{A}\op$, where $\mathcal{A} \subsetneq \Alg_\mathfrak{k}$ is the full subcategory of $\mathfrak{k}$-algebras $A$ of finite type with $\nil(A) = \{0\}$.
\end{remark}
\subsubsection{Affine open subsets are a topology base}