Frobenius P-categories: the second definition

Abstract

21.1 Let P be a finite p-group; in this chapter we give an equivalent definition of a Frobenius P-category in terms of a P × P-set; as usual, we call P × P-set a set Ω endowed with a P × P-action, but we write u · ω · v instead of (u, v) · ω for any (u, v) ∈ P × P and any ω ∈ Ω. Although this definition is surprisingly simple — at least from our point of view — it does not reflect our motivation for considering such an object; however, this new definition is very suitable for the construction of localities (cf. 17.3) associated with a Frobenius P-category, as we show in chapters 22 and 23 below.