Localities associated with a Frobenius P-category
17.1 Let us come back to our abstract setting: let P be a finite p-group and F a P-category (cf. 2.2). In this chapter, we introduce the localities associated with F — which are extensions of the category F and generalize the “localités” associated with a finite group G having P as a Sylow p-subgroup, introduced in . As we explain in the Introduction (cf. I41), we are mainly interested in the possible existence and uniqueness of the perfect locality — defined in 17.13 below — for a Frobenius P-category, which to some extent generalizes the O-localité introduced in [35, Ch. VI]. But, we find other meaningful localities canonically associated with any Frobenius P-category, as the basic locality in chapter 22.
KeywordsFull Subcategory Structural Functor Group Homomorphism Abstract Setting Contravariant Functor
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