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On reflective subcategories of locally presentable categories

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J. Adamek and J. Rosicky

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 $\lambda = \aleph_0$ the answer is
affirmative also for all iso-full subcategories, i. e., those containing
with every pair of objects all isomorphisms between them. We discuss a
possible generalization of this from $\aleph_0$ to an arbitrary $\lambda$.

Keywords:
locally presentable category, reflective subcategory, elementary equivalence

2010 MSC:
18A40, 18C35

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 41, pp 1306-18.

Published 2015-10-05.

http://www.tac.mta.ca/tac/volumes/30/41/30-41.pdf

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