A categorical approach to additive combinatorics
Motivated by the definition of Freiman homomorphism we explore the possibilities of formulating some basic notions and techniques of additive combinatorics in a categorical language. We show that additive sets and Freiman homomorphisms form a category and we study several limit and colimit construct...
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| creator | Blanco, Saúl A Haghverdi, Esfandiar |
| description | Motivated by the definition of Freiman homomorphism we explore the
possibilities of formulating some basic notions and techniques of additive
combinatorics in a categorical language. We show that additive sets and Freiman
homomorphisms form a category and we study several limit and colimit
constructions in this, and in an interesting subcategory of this category.
Moreover, we study the additive structure of these (co)limit objects using
additive doubling constant. We relate this category to that of finite sets and
mappings, and that of abelian groups and group homomorphisms. We show that the
Konyagin \& Lev result on universal ambient groups is an instance of
adjunction. |
| doi_str_mv | 10.48550/arxiv.2501.02097 |
| format | Article |
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possibilities of formulating some basic notions and techniques of additive
combinatorics in a categorical language. We show that additive sets and Freiman
homomorphisms form a category and we study several limit and colimit
constructions in this, and in an interesting subcategory of this category.
Moreover, we study the additive structure of these (co)limit objects using
additive doubling constant. We relate this category to that of finite sets and
mappings, and that of abelian groups and group homomorphisms. We show that the
Konyagin \& Lev result on universal ambient groups is an instance of
adjunction.</description><identifier>DOI: 10.48550/arxiv.2501.02097</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2025-01</creationdate><rights>http://creativecommons.org/licenses/by-nc-sa/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2501.02097$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2501.02097$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Blanco, Saúl A</creatorcontrib><creatorcontrib>Haghverdi, Esfandiar</creatorcontrib><title>A categorical approach to additive combinatorics</title><description>Motivated by the definition of Freiman homomorphism we explore the
possibilities of formulating some basic notions and techniques of additive
combinatorics in a categorical language. We show that additive sets and Freiman
homomorphisms form a category and we study several limit and colimit
constructions in this, and in an interesting subcategory of this category.
Moreover, we study the additive structure of these (co)limit objects using
additive doubling constant. We relate this category to that of finite sets and
mappings, and that of abelian groups and group homomorphisms. We show that the
Konyagin \& Lev result on universal ambient groups is an instance of
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possibilities of formulating some basic notions and techniques of additive
combinatorics in a categorical language. We show that additive sets and Freiman
homomorphisms form a category and we study several limit and colimit
constructions in this, and in an interesting subcategory of this category.
Moreover, we study the additive structure of these (co)limit objects using
additive doubling constant. We relate this category to that of finite sets and
mappings, and that of abelian groups and group homomorphisms. We show that the
Konyagin \& Lev result on universal ambient groups is an instance of
adjunction.</abstract><doi>10.48550/arxiv.2501.02097</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | A categorical approach to additive combinatorics |
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