On reflective subcategories of locally presentable categories

zbMATH Open1329.18003arXiv1504.03886MaRDI QIDQ3456334

Jiří Adámek, Jiří Rosický

Publication date: 14 December 2015

Abstract: Are all subcategories of locally finitely presentable categories that are closed under limits and $lambda$-filtered colimits also locally presentable? For full subcategories the answer is affirmative. Makkai and Pitts proved that in the case $lambda=alep{h}_0$ the answer is affirmative also for all iso-full subcategories, emph{i. hinspace e.}, those containing with every pair of objects all isomorphisms between them. We discuss a possible generalization of this from $alep{h}_0$ to an arbitrary $lambda$.

Full work available at URL: https://arxiv.org/abs/1504.03886

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zbMATH Keywords

locally presentable categoryreflective subcategory

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Accessible and locally presentable categories (18C35)

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