由Frobenius对产生的Hovey三元组

刘硕

doi:10.13371/j.cnki.chin.q.j.m.2021.02.006

数学季刊 >

2021 , Vol. 36 >Issue 2: 176 - 187

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.02.006

由Frobenius对产生的Hovey三元组

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College of Information Processing and Control Engineering, Lanzhou Petrochemical Polytechnic,
Lanzhou 730060, China

LIU Shuo (1983-), female, native of Shijiazhuang, Hebei, teacher of Lanzhou Petrochemical Polytechnic, engages in homological algebra and mathematics teaching.

收稿日期: 2020-09-01

网络出版日期: 2021-02-26

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A Hovey Triple Arising from a Frobenius Pair

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College of Information Processing and Control Engineering, Lanzhou Petrochemical Polytechnic,
Lanzhou 730060, China

LIU Shuo (1983-), female, native of Shijiazhuang, Hebei, teacher of Lanzhou Petrochemical Polytechnic, engages in homological algebra and mathematics teaching.

Received date: 2020-09-01

Online published: 2021-02-26

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摘要

We revisit Auslander-Buchweitz approximation theory and fifind some relations

with cotorsion pairs and model category structures. From the notion of weak-cogenerators,

we introduce the concept of Frobenius pair (X ,ω) in a triangulated category T . We show

how to construct from a Frobenius pair (X ,ω) a triangulated model structure on X ^∧.

关键词： Triangulated category; Weak-cogenerator; Approximation theory; Frobenius
pair; Model category structures

本文引用格式

刘硕 . 由Frobenius对产生的Hovey三元组[J]. 数学季刊, 2021 , 36(2) : 176 -187 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.006

Abstract

We revisit Auslander-Buchweitz approximation theory and fifind some relations

with cotorsion pairs and model category structures. From the notion of weak-cogenerators,

we introduce the concept of Frobenius pair (X ,ω) in a triangulated category T . We show

how to construct from a Frobenius pair (X ,ω) a triangulated model structure on X ^∧.

Key words： Triangulated category; Weak-cogenerator; Approximation theory; Frobenius
pair; Model category structures

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