Geodesic
A finitary adjoint functor theorem
Theory and applications of categories, Tome 41 (2024), pp. 1919-1936.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

Graduated locally finitely presentable categories are introduced, examples include categories of sets, vector spaces, posets, presheaves and Boolean algebras. A finitary functor between graduated locally finitely presentable categories is proved to be a right adjoint if and only if it preserves countable limits. For endofunctors on vector spaces or pointed sets even countable products are sufficient. Surprisingly, for set functors there is a single exception of a (trivial) finitary functor preserving countable products but not countable limits.
Publié le :
Classification : 18A22, 18A35, 18A40, 18B05
Keywords: Locally finitely presentable categories, finitary functors 
@article{TAC_2024_41_a52,
     author = {Ji\v{r}{\'\i} Ad\'amek and Lurdes Sousa},
     title = {A finitary adjoint functor theorem},
     journal = {Theory and applications of categories},
     pages = {1919--1936},
     publisher = {mathdoc},
     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a52/}
}
TY  - JOUR
AU  - Jiří Adámek
AU  - Lurdes Sousa
TI  - A finitary adjoint functor theorem
JO  - Theory and applications of categories
PY  - 2024
SP  - 1919
EP  - 1936
VL  - 41
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2024_41_a52/
LA  - en
ID  - TAC_2024_41_a52
ER  - 
%0 Journal Article
%A Jiří Adámek
%A Lurdes Sousa
%T A finitary adjoint functor theorem
%J Theory and applications of categories
%D 2024
%P 1919-1936
%V 41
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2024_41_a52/
%G en
%F TAC_2024_41_a52
Jiří Adámek; Lurdes Sousa. A finitary adjoint functor theorem. Theory and applications of categories, Tome 41 (2024), pp. 1919-1936. http://geodesic.mathdoc.fr/item/TAC_2024_41_a52/