On bornological semi-abelian algebras

Document Type: Research Paper

Authors

1 Universit'e de Louvain, Belgium.

2 Department of Mathematics, University of Coimbra, Portugal.

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.

Keywords


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