Timeline for When does the categorical definition of a module work?
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| Jul 9, 2013 at 0:44 | comment | added | Jacob Lurie | It seems worth pointing out that the discussion in my thesis contains a mistake. Theorem 3.1.6 is false as stated: if $A$ is a simplicial commutative ring, you generally cannot recover the $\infty$-category of $A$-modules by stabilizing the $\infty$-category of $A$-algebras. Consequently, the theory of derived algebraic geometry (based on simplicial commutative rings) should probably be regarded as a setting where the "categorical" notion of module doesn't work (or at least doesn't recover the usual notion of module), unless you work in characteristic zero or use $E_{\infty}$-rings instead. | |
| Jul 6, 2013 at 15:13 | history | answered | John Salvatierrez | CC BY-SA 3.0 |