On reflective subcategories of locally presentable categories

preprint2015arXivOpen access

Abstract

Are all subcategories of locally finitely presentable categories that are closed under limits and λλ-filtered colimits also locally presentable? For full subcategories the answer is affirmative. Makkai and Pitts proved that in the case λ=ℵ0λ=\aleph_0 the answer is affirmative also for all iso-full subcategories, \emph{i.\thinspace e.}, those containing with every pair of objects all isomorphisms between them. We discuss a possible generalization of this from ℵ0\aleph_0 to an arbitrary λλ.

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