Looking for a perfect Fsc-locality

Part of the Progress in Mathematics book series (PM, volume 274)


24.1 Let P be a finite p-group and F a Frobenius P-category. In the previous chapter, we already have given a sufficient condition for the existence and the uniqueness of a perfect Fsc-locality Lsc as a sublocality of the reduced Fsc-locality Lr, sc; as we point out in Remark 23.35, in this case Proposition 3.1 in [13] already provides a complete proof of the uniqueness of Lsc. In this last chapter, we prove that any perfect Fsc-locality has to be a sublocality of Lr, sc independently of any condition; in particular, when our sufficient condition is fulfilled, this provides another proof of the uniqueness of Lsc. From now on, (τsc, Lsc, πsc) is a perfect Fsc-locality Lsc; recall that the structural functor πsc: LscFsc induces an equivalence of categories
$$ \tilde {L}^{{\text{sc}}} \cong \tilde {F}^{sc} $$
between their respective exterior quotients (cf. 1.3); we write τ and π for short. We will consider the additive cover (Fsc) of Fsc (cf. A2.7 and A4.10).


Structural Functor Complete Proof Additive Cover Previous Chapter Canonical Morphism 
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© Birkhäuser Verlag AG 2009

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