Geodesic
On reflective subcategories of locally presentable categories
Theory and applications of categories, Tome 30 (2015), pp. 1306-18

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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 $\lambda$.

Publié le :
Classification : 18A40, 18C35
Keywords: locally presentable category, reflective subcategory, elementary equivalence 
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     author = {J. Adamek and J. Rosicky},
     title = {On reflective subcategories of locally presentable categories},
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     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a40/}
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J. Adamek; J. Rosicky. On reflective subcategories of locally presentable categories. Theory and applications of categories, Tome 30 (2015), pp. 1306-18. http://geodesic.mathdoc.fr/item/TAC_2015_30_a40/