On bornological semi-abelian algebras

If T is a semi-abelian algebraic theory, we prove that the category BornT of bornological T-algebras is homological with semi-direct products. We give a formal criterion for the representability of actions in BornT and, for a bornological T-algebra X, we investigate the relation between the represen...

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Bibliographic Details
Main Author: Borceux, Francis (author)
Other Authors: Clementino, Maria Manuel (author)
Format: article
Language:eng
Published: 2021
Subjects:
Semi-abelian algebraic theory
bornology
bornological algebra
bornological group
action representability
algebraic coherence
local algebraic cartesian closedness
Online Access:http://hdl.handle.net/10316/101221
Country:Portugal
Oai:oai:estudogeral.sib.uc.pt:10316/101221
Description
Summary:If T is a semi-abelian algebraic theory, we prove that the category BornT of bornological T-algebras is homological with semi-direct products. We give a formal criterion for the representability of actions in BornT and, for a bornological T-algebra X, we investigate the relation between the representability of actions on X as a T-algebra and as a bornological T- algebra. We investigate further the algebraic coherence and the algebraic local cartesian closedness of BornT and prove in particular that both properties hold in the case of bornological groups.

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