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Questions tagged [derived-functors]

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20
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1answer
776 views

Example of an additive functor admitting no right derived functor

I asked the same question a week ago on Mathematics Stackexchange but got no answer. What would be a simple example of an additive functor $F:\mathcal C\to\mathcal C'$ of abelian categories such that ...
5
votes
0answers
327 views

Description of connecting maps of Derived functors

Let $C$ be an abelian category with enough injectives and $F$ be a left exact additive functor. Consider the short exact sequence $0 \to A' \to A \to A ''\to 0$. Therefore, we have connecting maps $\...
5
votes
1answer
364 views

Different definitions of derived functors

In principle one uses the notion of derived category, and the other doesn't. Suppose $F: \mathcal A \to \mathcal B$ is a left exact (additive) functor between abelian categories, and suppose the ...
4
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2answers
717 views

Two basic questions on derived categories

Let $\mathcal{A}, \mathcal{B}$ be two abelian categories with sufficiently many injective objects (in my case these are categories of sheaves of vector spaces on a manifold). Let $f_*\colon \mathcal{A}...