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arXiv · 1812.10649

Colimit-Dense Subcategories

J. Adámek·A. Brooke-Taylor·T. Campion·L. Positselski·J. Rosický
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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 $3$-element set is colimit-dense in $\Set^{\op}$, and spaces of countable dimension are colimit-dense in $\Vec^{op}$.

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J. Adámek, A. Brooke-Taylor, T. Campion, L. Positselski, J. Rosický. 2018-12-27. Colimit-Dense Subcategories. https://arxiv.org/abs/1812.10649

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