A finitary adjoint functor theorem (Preprint)

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Type: Preprint
National /International: International
Title: A finitary adjoint functor theorem
Publication Date: 2023-11-23
Authors: - Jirí Adámek
- Lurdes Sousa

Ranked locally finitely presentable categories are introduced, examples include categories of sets, vector spaces, posets, presheaves and boolean algebras. A finitary functor between ranked 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.

Institution: DMUC 23-35
Online version: http://www.mat.uc.pt...prints/eng_2023.html
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