3 papers
math.CT2026
On the Semi-Abelianness of Affine Group Schemes
David Forsman
We prove that the category of commutative Hopf algebras over a field is co-semi-abelian. Consequently, the category of affine group -schemes is semi-abelian. We establish co…
math.CT2025
A Categorical Approach to Finiteness Conditions
David Forsman
We introduce a general categorical framework for finiteness conditions that unifies classical notions such as Noetherianness, Artinianness, and various forms of topological compact…
math.LO2025
Semi-abelian by Design: Johnstone Algebras Unifying Implication and Division
David Forsman
Johnstone demonstrated that Heyting semilattices form a semi-abelian category via a specific triple of terms. Inspired by this work, we introduce \emph{Johnstone algebras} or J-alg…