  Let $A$ be a ring, and let $M$ and $N$ be $A$-modules. Then $N$ can be viewed
as a group object in the category $A$-Mod/$M$ of $A$-modules over $M$ and
Ext$^1(M, N)$ can be interpreted as the set of isomorphism classes of
$N$-torsors. Alternatively, $M$ can be viewed as a cogroup object in the
category $N$/$A$-Mod of $A$-modules under $N$ and Ext$^1(M, N)$ can be
interpreted as the set of isomorphism classes of $M$-cotorsors.
