A natural fibration for rings

Abstract

A ringed partially ordered set with zero is a pair (L,F ), where L is a partially ordered set with a least element 0L and F : L → Ring is a covariant functor. Here the partially ordered set L is given a category structure in the usual way and Ring denotes the category of associative rings with identity. Let RingedParOrd0 be the category of ringed partially ordered sets with zero. There is a functor H : Ring → RingedParOrd0 that associates to any ring R a ringed partially ordered set with zero (Hom(R), FR). The functor H has a left inverse Z : RingedParOrd0 → Ring. The category RingedParOrd0 is a fibred category. Mathematics Subject Classification (2010). Primary 18D30.