Finitely presentable morphisms in exact sequences
Author's Department
Mathematics & Actuarial Science Department
Document Type
Research Article
Publication Title
Theory and Applications of Categories
Publication Date
6-4-2010
Abstract
Let K be a locally finitely presentable category. If K is abelian and the sequence, we show that 1) K is finitely generated ⇔ c is finitely presentable; 2) k is finitely presentable ⇔ C is finitely presentable. The "â‡" directions fail for semi-abelian varieties. We show that all but (possibly) 2)(â‡) follow from analogous properties which hold in all locally finitely presentable categories. As for 2)(â‡), it holds as soon as K is also co-homological, and all its strong epimorphisms are regular. Finally, locally finitely coherent (resp. noetherian) abelian categories are characterized as those for which all finitely presentable morphisms have finitely generated (resp. presentable) kernel objects. © Michel Hébert, 2010.
First Page
209
Last Page
220
Recommended Citation
APA Citation
Hébert, M.
(2010). Finitely presentable morphisms in exact sequences. Theory and Applications of Categories, 24, 209–220.
https://fount.aucegypt.edu/faculty_journal_articles/690
MLA Citation
Hébert, Michel
"Finitely presentable morphisms in exact sequences." Theory and Applications of Categories, vol. 24, 2010, pp. 209–220.
https://fount.aucegypt.edu/faculty_journal_articles/690