Alexei Pirkovskii

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seen Jan 9 at 10:02

Jun
19
comment When an exact embedding of abelian categories induces a full embedding of their derived categories?
Sorry, of course I meant that $\mathrm{Tor}_0^A(B,B)\cong B$, not $A$.
Jun
19
comment When an exact embedding of abelian categories induces a full embedding of their derived categories?
When the categories are module categories, and the functor is restriction along a map $A\to B$ of rings, $D^b(B)\to D^b(A)$ is a full embedding iff [ \mathrm{Tor}_i^A(B,B)\cong \begin{cases} A, & i=0,\\ 0, & i>0. \end{cases} ] See W. Geigle and H. Lenzing, "Perpendicular categories with applications to representations and sheaves", J. Algebra 144 (1991), no. 2, 273--343.
Dec
19
awarded  Necromancer
Dec
19
answered expository papers related to quantum groups
Dec
19
awarded  Teacher
Dec
19
answered Grothendieck on Topological Vector Spaces