论文标题
torsor-cotorsor二元性二重性
Torsor-cotorsor duality of Ext groups
论文作者
论文摘要
让$ a $为戒指，让$ m $和$ n $为$ a $ modules。然后，$ n $可以将$ a $ mod/$ m $ a $ a $ a $ modules视为$ m $ $ m $和ext $^1（m，n）$的组对象。另外，可以将$ m $视为$ n $/$ a $ a $ a $ a $ modules y $ n $和ext $^1（m，n）$的类别中的cogroup对象。
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.
