Triangulated functors, homological functors, tilts, and lifts
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Let T be a triangulated category and let X be an object of T. This paper studies the questions: Does there exist a triangulated functor G : D(ℤ) T with G(ℤ)≌X? Does there exist a triangulated functor H : T D(ℤ) with h0 ⊚ H ⋍ HomT (X, −)? To what extent are G and H unique?
One spin off is a proof that the homotopy category of spectra is not the stable category of any Frobenius category with set indexed coproducts.
KeywordsHomological Functor Homotopy Category Stable Category Frobenius Category Triangulate Functor
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