6 papers
A Syntactic Approach to Ulmer's Bialgebras
David Forsman
Ulmer introduced a semantic notion of bialgebras that unifies a broad class of algebraic and coalgebraic structures. We develop a syntactic counterpart by introducing signature pai…
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…
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…
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…
On the Multicategorical Meta-Theorem and the Completeness of Restricted Algebraic Deduction Systems
David Forsman
Eight categorical soundness and completeness theorems are established within the framework of algebraic theories. Exactly six of the eight deduction systems exhibit complete semant…
Functors of Variance: Heuristic Naturality and Connection to Ends
David Forsman
The concept of a variance on a category is introduced as a two-sided strict factorization system. By employing variances, we define functors of variance in a more general setting t…