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

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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 
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     author = {Ji\v{r}{\'\i} Ad\'amek and Lurdes Sousa},
     title = {A finitary adjoint functor theorem},
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     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a52/}
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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/