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"Quiver" is the word used for "directed graph" in some parts of representation theory. The main reason to use the term quiver is to indicate an interest in considering representations of the quiver.

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How to compute the derived functor of bounded derived categories of hereditary algebra?

Let $\Lambda$ be a finite dimensional algebra given by the quiver $$\cdot\leftarrow\cdot\leftarrow\cdot\rightarrow\cdot.$$ It can be view as an triangulated matrix algebra. $$\Lambda={A\ \ M\choose0\ …