A Finitary Adjoint Functor Theorem
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914665735389184 |
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| author | Adámek, Jirí Sousa, Lurdes |
| author_facet | Adámek, Jirí Sousa, Lurdes |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14965 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Finitary Adjoint Functor Theorem Adámek, Jirí Sousa, Lurdes Category Theory 18A22, 18A35, 18A40, 18B05 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. |
| title | A Finitary Adjoint Functor Theorem |
| topic | Category Theory 18A22, 18A35, 18A40, 18B05 |
| url | https://arxiv.org/abs/2311.14965 |