A natural fibration for rings

Bosi, Alessandro Andrea; Facchini, Alberto

doi:10.4171/rsmup/76

Bosi, Alessandro Andrea ; Facchini, Alberto

Rendiconti del Seminario Matematico della Università di Padova, Tome 145 (2021), pp. 167-180.

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Résumé

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 $F : L \to 𝖱𝗂𝗇𝗀$ 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 $ℋ : 𝖱𝗂𝗇𝗀 \to {𝖱𝗂𝗇𝗀𝖾𝖽𝖯𝖺𝗋𝖮𝗋𝖽}_{0}$ that associates to any ring $R$ a ringed partially ordered set with zero $(Hom (R), F_{R})$ . The functor $ℋ$ has a left inverse $Z : {𝖱𝗂𝗇𝗀𝖾𝖽𝖯𝖺𝗋𝖮𝗋𝖽}_{0} \to 𝖱𝗂𝗇𝗀$ . The category ${𝖱𝗂𝗇𝗀𝖾𝖽𝖯𝖺𝗋𝖮𝗋𝖽}_{0}$ is a fibred category.

Publié le : 2021-05-03

MR Zbl

DOI : 10.4171/rsmup/76

Classification : 18, 00

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     author = {Bosi, Alessandro Andrea and Facchini, Alberto},
     title = {A natural fibration for rings},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {167--180},
     volume = {145},
     year = {2021},
     doi = {10.4171/rsmup/76},
     mrnumber = {4261651},
     zbl = {1497.16046},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/76/}
}

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Bosi, Alessandro Andrea; Facchini, Alberto. A natural fibration for rings. Rendiconti del Seminario Matematico della Università di Padova, Tome 145 (2021), pp. 167-180. doi : 10.4171/rsmup/76. http://www.numdam.org/articles/10.4171/rsmup/76/

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