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For questions about the derived categories of various abelian categories and questions regarding the derived category construction itself.

15 votes
Accepted

Example of an additive functor admitting no right derived functor

Let ${\cal C}$ be the category of finite dimensional ${\bf Z}/2$-vector spaces equipped with a ${\bf Z}/2$ action, let ${\cal C'}$ be the category of finite dimensional ${\bf Z}/2$-vector spaces and l …
Yonatan Harpaz's user avatar
10 votes
Accepted

Different definitions of derived functors

The total right derived functor ${\bf R}F(-)$ contains a bit more information than just its individual cohomologies ${\bf R}^iF(-) = H^i({\bf R}F(-))$. This information can indeed be described as a ki …
Yonatan Harpaz's user avatar
6 votes
Accepted

The naive approach to deriving profunctors - What's wrong with it?

The problem with this definition is that the formula $\mathrm{colim}_{X \to Z \in \mathcal{W}} F(Z)$ does not, in general, depend functorially on $X$. For it to depend functorially on $X$ you need a w …
Yonatan Harpaz's user avatar