For categories and groups we feel at ease with the constructions, and we know that we can recover the original group or category fram the associated space. But what happens if we try to apply the same kind of ideas to algebraic systems with very much structure? In particular, what happens when we try to encode n-categories? I will try to show that the really old constructions - when suitably interpreted - are quite sufficient for these applications. In fact, an n-category can be seen as nothing but a "polynomial functor of degree n" satisfying some reasonable conditions.

If the audience prefers, I'll talk about various categories of finitely generated free A-modules for A an S-algebra instead.