Jiří Adámek, Andrew D. Brooke-Taylor, Tim Campion, Leonid Positselski, Jiří Rosický
Colimit-dense subcategories

Comment.Math.Univ.Carolin. 60,4 (2019) 447-462.

Abstract:Among cocomplete categories, the locally presentable ones can be defined as those with a strong generator consisting of presentable objects. Assuming Vop\v enka'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 ${\mathbf{Vec}}^{\rm op}$.

Keywords: locally presentable category; colimit-dense subcategory; Vopěnka's Principle

DOI: DOI 10.14712/1213-7243.2019.021
AMS Subject Classification: 18C35 18A30 03E55