# A natural fibration for rings

### Alessandro Andrea Bosi

Università di Roma Tre, Italy### Alberto Facchini

Università di Padova, Italy

## Abstract

A ringed partially ordered set with zero is a pair $(L,F)$, where $L$ is a partially ordered set with a least element $0_{L}$ 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 $RingedParOrd_{0}$ be the category of ringed partially ordered sets with zero. There is a functor $H:Ring→RingedParOrd_{0}$ that associates to any ring $R$ a ringed partially ordered set with zero $(Hom(R),F_{R})$. The functor $H$ has a left inverse $Z:RingedParOrd_{0}→Ring$. The category $RingedParOrd_{0}$ is a fibred category.

## Cite this article

Alessandro Andrea Bosi, Alberto Facchini, A natural fibration for rings. Rend. Sem. Mat. Univ. Padova 145 (2021), pp. 167–180

DOI 10.4171/RSMUP/76