A ringed partially ordered set with zero is a pair , where is a partially ordered set with a least element and is a covariant functor. Here the partially ordered set is given a category structure in the usual way and denotes the category of associative rings with identity. Let be the category of ringed partially ordered sets with zero. There is a functor that associates to any ring a ringed partially ordered set with zero . The functor has a left inverse . The category is a fibred category.
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Alessandro Andrea Bosi, Alberto Facchini, A natural fibration for rings. Rend. Sem. Mat. Univ. Padova 145 (2021), pp. 167–180DOI 10.4171/RSMUP/76