Adámek, J, Brooke-Taylor, AD orcid.org/0000-0003-3734-0933, Campion, T et al. (2 more authors) (2020) Colimit-dense subcategories. Commentationes Mathematicae Universitatis Carolinae, 60 (4). pp. 447-462. ISSN 0010-2628
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 ${\mathbf{Vec}}^{\rm op}$.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Locally presentable category; colimit-dense subcategory; Vopěnka's Principle |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Apr 2019 10:07 |
Last Modified: | 28 Feb 2020 14:25 |
Status: | Published |
Publisher: | Faculty of Mathematics and Physics of Charles University |
Identification Number: | 10.14712/1213-7243.2019.021 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:144755 |