Avsnittsöversikt
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We showed that bounded below complexes have injective resolutions (if there are enough injectives). We also showed that K^+(I) -> D^+(A) is an equivalence. More precisely, if I is a bounded below injective complex, then morphisms A -> I in the derived category, i.e. roofs, are the same thing as morphisms A -> I in the homotopy category, i.e., morphisms of complexes up to homotopy.
References:
- Huybrechts 2.29–2.40, 2.44
- Gelfand–Manin III 5.20–25, III 6.1–2