Adjusted mean value theorem.

This commit is contained in:
Bokuan Li
2026-02-03 11:07:32 -05:00
parent 04786ba3d9
commit 7bbbf75213
3 changed files with 31 additions and 9 deletions

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@@ -142,7 +142,7 @@ Let $\catc$ be a category and $(\seqi{A}, \bracsn{f^i_j| i, j \in I, i \lesssim
\end{definition}
\begin{proposition}
\label{proposition:direct-limit}
\label{proposition:module-direct-limit}
Let $R$ be a ring and $(\seqi{A}, \bracsn{T^i_j| i, j \in I, i \lesssim j})$ be an upward-directed system of $R$-modules, then there exists $(A, \bracsn{T^i_A}_{i \in I})$ such that:
\begin{enumerate}
\item For each $i \in I$, $T^i_A \in \hom({A_i, A})$.