Abstract.
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.
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Received: 8 March 2002 / Revised version: 18 October 2002 Published online: 14 February 2003
Mathematics Subject Classification (2000): 18E30, 55U35
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Jørgensen, P. Triangulated functors, homological functors, tilts, and lifts. manuscripta math. 110, 381–406 (2003). https://doi.org/10.1007/s00229-002-0350-4
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DOI: https://doi.org/10.1007/s00229-002-0350-4