Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Created Beck module, mentioned it (once) on the tangent category page.
There was work done on the ‘derived module’ of a group homomorphism in
R. H. Crowell, The derived module of a homomorphism, Advances in Math., 5, (1971), 210 – 238.
This is related to both Beck modules and to Fox derivatives. (i discussed this in the Menagerie, and it relates to the linearisation of crossed complexes in Ronnie Brown’s work.)
Very nice! I have added a few more pointers to this from other relevant entries.
I have also added pointer to Beck 67.
Added a reference to a preprint by Markus Szymik relating Beck modules of quandles to the detection of the unknot. NB: Richard, he is at Trondheim.
Hehe, yes, Markus and I were colleagues for a while, and meet occasionally :-). He is a very nice chap! I believe is on sabbatical at the moment, in Cambridge I think.
Let $A$ be a commutative ring, and let $M$ be an $A$-module. Then any square-zero extension $B\to A$ with kernel $M$ can be viewed as a torsor in $\text{CRing}/A$ for the abelian group object $A\oplus M\to A$ corresponding to $M$. The group action $(A\oplus M)\times_A B\to B$ is such that $((a, m), b)$ is mapped to $b+m$.
Is every torsor for $A\oplus M\to A$ necessarily a square-zero extension? More specifically, is the category of torsors for $A\oplus M\to A$ equivalent to the category of square-zero extensions of $A$ by $M$?
1 to 7 of 7