Torsor-cotorsor duality of Ext groups

Nicholas Mertes

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arXiv · 2006.15996

Torsor-cotorsor duality of Ext groups

Nicholas Mertes

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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.

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Nicholas Mertes. 2020-06-25. Torsor-cotorsor duality of Ext groups. https://arxiv.org/abs/2006.15996

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