# Tag Info

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### What is a triangle?

To answer your first precise questions: Yes, every distinguished triangle in $D(A)$ comes from a short exact sequence. For every distinguished triangle $X \to Y \to \mathrm{Cone}(f) \stackrel{+1}\to$...
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Accepted

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### Why is the derived tensor product only defined for bounded above derived categories?

I would like to add my 2 euro ¢. In a nutshell: your information is outdated. "Residues and Duality" by Hartshorne was the first available text on derived categories of coherent sheaves and ...
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### What (if anything) unifies stable homotopy theory and Grothendieck's six functors formalism?

You can certainly form a category of sheaves of spectra on a space that is quite analogous to the derived category of sheaves of chain complexes. Roughly speaking, a presheaf of spectra is a called a (...
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