A natural fibration for rings

  • Alessandro Andrea Bosi

    Università di Roma Tre, Italy
  • Alberto Facchini

    Università di Padova, Italy
A natural fibration for rings cover
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Abstract

A ringed partially ordered set with zero is a pair (L,F)(L,F), where LL is a partially ordered set with a least element 0L0_L and F ⁣:LRingF\colon L\to\mathsf{Ring} is a covariant functor. Here the partially ordered set LL is given a category structure in the usual way and Ring\mathsf{Ring} denotes the category of associative rings with identity. Let RingedParOrd0\mathsf{RingedParOrd}_0 be the category of ringed partially ordered sets with zero. There is a functor H ⁣:RingRingedParOrd0\mathcal{H}\colon\mathsf{Ring}\to\mathsf{RingedParOrd}_0 that associates to any ring RR a ringed partially ordered set with zero (Hom(R),FR)(\mathrm{Hom}(R),F_R). The functor H\mathcal{H} has a left inverse Z ⁣:RingedParOrd0RingZ\colon\mathsf{RingedParOrd}_0\to\mathsf{Ring}. The category RingedParOrd0\mathsf{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