How Large Are Left Exact Functors?
نویسندگان
چکیده
For a broad collection of categories K, including all presheaf categories, the following statement is proved to be consistent: every left exact (i.e. finite-limits preserving) functor from K to Set is small, that is, a small colimit of representables. In contrast, for the (presheaf) category K = Alg(1, 1) of unary algebras we construct a functor from Alg(1, 1) to Set which preserves finite products and is not small. We also describe all left exact set-valued functors as directed unions of “reduced representables”, generalizing reduced products.
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