On the Semi-Abelianness of Affine Group Schemes

Fuente: arXiv
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Autor principal: Forsman, David
Formato: Preprint
Publicado: 2026
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author Forsman, David
author_facet Forsman, David
contents We prove that the category of commutative Hopf algebras over a field $k$ is co-semi-abelian. Consequently, the category of affine group $k$-schemes is semi-abelian. We establish coregularity by identifying the orthogonal factorization system of surjections and faithfully flat injections, and we deduce coexactness from Takeuchi's correspondence between normal Hopf ideals and Hopf subalgebras of commutative Hopf $k$-algebras.
format Preprint
id arxiv_https___arxiv_org_abs_2602_21060
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On the Semi-Abelianness of Affine Group Schemes
Forsman, David
Category Theory
Algebraic Geometry
Rings and Algebras
We prove that the category of commutative Hopf algebras over a field $k$ is co-semi-abelian. Consequently, the category of affine group $k$-schemes is semi-abelian. We establish coregularity by identifying the orthogonal factorization system of surjections and faithfully flat injections, and we deduce coexactness from Takeuchi's correspondence between normal Hopf ideals and Hopf subalgebras of commutative Hopf $k$-algebras.
title On the Semi-Abelianness of Affine Group Schemes
topic Category Theory
Algebraic Geometry
Rings and Algebras
url https://arxiv.org/abs/2602.21060