Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 14 1 2021 01 01 On bornological semi-abelian algebras 181 222 87514 10.29252/cgasa.14.1.181 EN Francis Borceux Universit\'e de Louvain, Belgium. Maria Manuel Clementino Department of Mathematics, University of Coimbra, Portugal. Journal Article 2020 06 07 If $\Bbb T$ is a semi-abelian algebraic theory, we prove that the category ${\rm Born}^{\Bbb T}$ of bornological $\Bbb T$-algebras is homological with semi-direct products. We give a formal criterion for the representability of actions in ${\rm Born}^{\Bbb T}$ and, for a bornological $\Bbb T$-algebra $X$, we investigate the relation between the representability of actions on $X$ as a $\Bbb T$-algebra and as a bornological $\Bbb T$-algebra. We investigate further the algebraic coherence and the algebraic local cartesian closedness of ${\rm Born}^{\Bbb T}$ and prove in particular that both properties hold in the case of bornological groups. https://cgasa.sbu.ac.ir/article_87514_6bd7fb9a1c7583f5b8f3b7873d4350bb.pdf