Let $X$ be a rack and $A$ be an $X$-module. By this paper, p. 33, we can associate a cochain complex $C^\bullet(X,A)$ to the pair $(X,A)$. This complex is explicitly defined by a differential $d$. I wonder if the cohomology $H^\bullet(X,A)$ of the complex has an interpretation as derived functor cohomology. What functor from $X$-modules to $X$-modules do we have to derive? And how to show then the equivalence of the two definitions? I think the analogy to group cohomology is not very helpful, or can we somehow define the invariants of an $X$-module and make it fit?
$\begingroup$
$\endgroup$
2
asked Apr 18, 2021 at 10:10
-
2$\begingroup$ If it is a derived functor, it's the derived functor of H^0. I'm not sure if this helps though :) $\endgroup$– Denis NardinCommented Apr 18, 2021 at 10:46
-
$\begingroup$ You are right, thank you. $\endgroup$– Christoph MarkCommented Apr 18, 2021 at 11:02
Add a comment
|