@article { author = {Borceux, Francis and Clementino, Maria Manuel}, title = {On bornological semi-abelian algebras}, journal = {Categories and General Algebraic Structures with Applications}, volume = {14}, number = {1}, pages = {181-222}, year = {2021}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {10.29252/cgasa.14.1.181}, 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 = {Semi-abelian algebraic theory,bornology,bornological algebra,bornological group,action representability,algebraic coherence,local algebraic cartesian closedness}, url = {https://cgasa.sbu.ac.ir/article_87514.html}, eprint = {https://cgasa.sbu.ac.ir/article_87514_6bd7fb9a1c7583f5b8f3b7873d4350bb.pdf} }