2023/11/25 by Adámek, Jirí, Sousa, Lurdes
#18A22 #18A35 #18A40 #18B05 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.14965
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.