Avsnittsöversikt
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We constructed the derived category. In particular, we showed that every zig-zag of quasi-isomorphisms and morphisms could be refined to a roof A <- C -> B where C -> A is a quasi-isomorphism. That is, the quasi-isomorphisms of the homotopy category K(A) admits a left calculus of fractions. We also showed that we have a fully faithful functor A -> D(A) identifying A with the complexes X in D(A) such that H^i(X)=0 for all i\neq 0.
References:
- Gelfand–Manin, Ch III.2–III.4 (and III.5.2)
- Huybrechts, Ch 2, 2.1–2.33