A precise concept of concrete geometrical category is introduced in an axiomatic way. To any algebra L for an many-sorted infinitary algebraic theory T is associated a concrete geometrical category Geo(L), the so-called classifying concrete geometrical category of L, satisfying a universal property. The terminology "geometrical" is justified firstly for Geo(L) and secondly for any concrete geom...

1 Characteristic 0 We start with a basic question: given a polynomial f ∈ C[z1, · · · , zn] with a singularity at 0, how can we measure the “singularness” of this polynomial in a precise way? In other words: we can look at various singularities and see intuitively that some singularities are worse than others. For instance, it feels like a transverse self-intersection is probably not as bad as ...