Add AB6 and AB6* conditions to injectives.tex

injectives.tex

@@ -1276,12 +1276,14 @@ \section{Grothendieck's AB conditions}
 \item[AB3] $\mathcal{A}$ has direct sums,
 \item[AB4] $\mathcal{A}$ has AB3 and direct sums are exact,
 \item[AB5] $\mathcal{A}$ has AB3 and filtered colimits are exact.
+\item[AB6] $\mathcal{A}$ has AB3 and small products distribute over filtered colimits: for a small diagram $J$ and a collection of $J$-indexed filtered diagrams $I_{j}$ for $j\in J$ the natural map $\colim_{(i_{j}\in I_{j})_{j}}\prod_{j\in J}M_{i_{j}}\to\prod_{j\in J}\colim_{i_{j}\in I_{j}}M_{i_{j}}$ is an isomorphism. 
 \end{enumerate}
 Here are the dual notions
 \begin{enumerate}
 \item[AB3*] $\mathcal{A}$ has products,
 \item[AB4*] $\mathcal{A}$ has AB3* and products are exact,
 \item[AB5*] $\mathcal{A}$ has AB3* and cofiltered limits are exact.
+\item[AB6*] $\mathcal{A}$ has AB3* and direct sums distribute over cofiltered limits: for a small diagram $J$ and a collection of $J$-indexed cofiltered diagrams $I_{j}$ for $j\in J$ the natural map $\bigoplus_{j\in J}\lim_{i_{j}\in I_{j}}M_{i_{j}}\to\lim_{(i_{j}\in I_{j})_{j}}\bigoplus_{j\in J}M_{i_{j}}$ is an isomorphism. 
 \end{enumerate}
 We say an object $U$ of $\mathcal{A}$ is a {\it generator} if
 for every $N \subset M$, $N \not = M$ in $\mathcal{A}$ there exists a morphism