On Pseudofunctors Sending Groups to 2-Groups

被引：0

作者：

Alan S. Cigoli

Sandra Mantovani

Giuseppe Metere

机构：

[1] Università degli Studi di Torino,Dipartimento di Matematica “Giuseppe Peano”

[2] Università degli Studi di Milano,Dipartimento di Matematica “Federigo Enriques”

[3] Università degli Studi di Palermo,Dipartimento di Matematica e Informatica

来源：

Mediterranean Journal of Mathematics | 2023年 / 20卷

关键词：

Pseudofunctor; internal groups; 2-groups; monoidal opfibration; 18C40; 18D30; 18G45; 18M05;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

For a category B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textsf{B}}$$\end{document} with finite products, we first characterize pseudofunctors from B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textsf{B}}$$\end{document} to Cat\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}\textsf{at}$$\end{document} whose associated opfibration is Cartesian monoidal. Among those, we then characterize the ones which extend to pseudofunctors from internal groups to 2-groups. If B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textsf{B}}$$\end{document} is additive, this is the case precisely when the associated opfibration has groupoidal fibres.

引用

共 20 条

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