From e0735ee92be85fa01f8324c371296ee91947ffcc Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Maximilian=20Ke=C3=9Fler?= Date: Wed, 16 Feb 2022 02:13:49 +0100 Subject: [PATCH] replace more hacks --- 2021_Algebra_I.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/2021_Algebra_I.tex b/2021_Algebra_I.tex index b2d0fab..2f5bc54 100644 --- a/2021_Algebra_I.tex +++ b/2021_Algebra_I.tex @@ -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}