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Results tagged with derived-categories
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user 51164
For questions about the derived categories of various abelian categories and questions regarding the derived category construction itself.
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 …
- 9,491
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 …
- 9,491
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 …
- 9,491