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Looking for a perfect Fsc-locality

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

Abstract

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
$$ \tilde {L}^{{\text{sc}}} \cong \tilde {F}^{sc} $$
(1)
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).

Keywords

Structural Functor Complete Proof Additive Cover Previous Chapter Canonical Morphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2009

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