The Weyl functor - Introduction to Absolute Arithmetic

Abstract

Starting from an ancient observation of Tits concerning the interpretation of symmetric groups as Chevalley groups over a (non-existing) field having only one element, we describe combinatorial geometry over this field, as well as Linear Algebra. We arrive at an "absolute mantra" which is one of the basic principles of the present book.

38 pages; submitted (June 2013) as a chapter in the monograph "Absolute Arithmetic and $\mathbb{F}_1$-Geometry" (ed. K. Thas)