Geodesic
Colimit-dense subcategories
Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 4, pp. 447-462.

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Among cocomplete categories, the locally presentable ones can be defined as those with a strong generator consisting of presentable objects. Assuming Vopěnka's Principle, we prove that a cocomplete category is locally presentable if and only if it has a colimit dense subcategory and a generator consisting of presentable objects. We further show that a $3$-element set is colimit-dense in ${\mathbf{Set}}^{\rm op}$, and spaces of countable dimension are colimit-dense in ${\mathbf{Vec}}^{\rm op}$.
DOI : 10.14712/1213-7243.2019.021
Classification : 03E55, 18A30, 18C35
Keywords: locally presentable category; colimit-dense subcategory; Vopěnka's Principle 
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     title = {Colimit-dense subcategories},
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Adámek, Jiří; Brooke-Taylor, Andrew D.; Campion, Tim; Positselski, Leonid; Rosický, Jiří. Colimit-dense subcategories. Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 4, pp. 447-462. doi : 10.14712/1213-7243.2019.021. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2019.021/

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