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Direct limits of a matrix and its transpose

Let $A \in M_n(\mathbb Z)$ and $A^T$ denote the transpose of $A$. Define the direct limits $$H_1 = \mathrm{colim} (\mathbb Z^n \xrightarrow{A} \mathbb Z^n \xrightarrow{A} \mathbb Z^n \xrightarrow{A} \...
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