On bornological semi-abelian algebras

Borceux, Francis;Clementino, Maria Manuel
(2021) Categories and General Algebraic Structures with Applications — Vol. 14, n° 1, p. 181-222 (2021)

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Authors
  • Borceux, FrancisUCLouvain
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  • Clementino, Maria Manuel
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Abstract
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.
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Borceux, F., & Clementino, M. M. (2021). On bornological semi-abelian algebras. Categories and General Algebraic Structures with Applications, 14(1), 181-222. https://doi.org/10.29252/cgasa.14.1.181 (Original work published 2021)