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fixed the formulas
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Leo Alonso
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It should be mentined that any localisation functor F: C -> D$F: C \to D$ induces a morphism Z[F]: Z[C] -> Z[D]$Z(F): Z(C) \to Z(D)$. A reference for this is Gabriel's thesis "Des categories abeliennes" (p. 446).

It should be mentined that any localisation functor F: C -> D induces a morphism Z[F]: Z[C] -> Z[D]. A reference for this is Gabriel's thesis "Des categories abeliennes" (p. 446).

It should be mentined that any localisation functor $F: C \to D$ induces a morphism $Z(F): Z(C) \to Z(D)$. A reference for this is Gabriel's thesis "Des categories abeliennes" (p. 446).

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It should be mentined that any localisation functor F: C -> D induces a morphism Z[F]: Z[C] -> Z[D]. A reference for this is Gabriel's thesis "Des categories abeliennes" (p. 446).