Colimit-Dense Subcategories
Category Theory
2020-12-04 v1
Abstract
Among cocomplete categories, the locally presentable ones can be defined as those with a strong generator consisting of presentable objects. Assuming Vop{\v{e}}nka's Principle, we prove that a cocomplete category is locally presentable iff it has a colimit dense subcategory and a generator consisting of presentable objects. We further show that a -element set is colimit-dense in \Set^{\op}, and spaces of countable dimension are colimit-dense in .
Cite
@article{arxiv.1812.10649,
title = {Colimit-Dense Subcategories},
author = {J. Adámek and A. Brooke-Taylor and T. Campion and L. Positselski and J. Rosický},
journal= {arXiv preprint arXiv:1812.10649},
year = {2020}
}