Unexpected properties of locally presentable categories

@article{Rosick1990UnexpectedPO,
  title={Unexpected properties of locally presentable categories},
  author={J. Rosick{\'y} and Vera Trnkov{\'a} and Jochen Adamek},
  journal={algebra universalis},
  year={1990},
  volume={27},
  pages={153-170}
}
Locally presentable categories are precisely those complete categories which have a small dense subcategory. Every subcategory of a locally presentable category (i) has a small dense subcategory, (ii) if it is closed under limits, then it is locally presentable and (iii) if it is closed under colimits, then it is coreflective. For density, canonical colimits can be substituted by arbitrary colimits.The above results hold under the assumption of the set-theoretical Vopenka's Principle; in fact… CONTINUE READING

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