Torsor-cotorsor duality of Ext groups

Abstract

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.

arXiv admin note: text overlap with arXiv:2006.04230

References in corpus (1)

• First order thickenings and cotorsors