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On the definition of triangulated categories
Triangulated categories were introduced in the 1960s by Grothendieck and Verdier in order to develop homological algebra in the framework of derived categories. An example of a triangulated category ...
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Switching left and right adjoints in recollement situations
In Fascieaux pervers, Beilinson, Bernstein and Deligne define a recollement situation as a triple of triangulated categories $\mathcal{D}_U,\mathcal{D}_F$ and $\mathcal{D}$, together with functors
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