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 andRing 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 categoryRingedParOrd0 is a fibred category.
A natural fibration for rings
Facchini A.
2021
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 andRing 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 categoryRingedParOrd0 is a fibred category.
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