### Abstract

For a small category K enriched over a suitable monoidal category V, the free completion of K under colimits is the presheaf category [K^{op}, V]. If K is large, its free completion under colimits is the V-category P K of small presheaves on K, where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed structures on P K.

Original language | English |
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Pages (from-to) | 651-663 |

Number of pages | 13 |

Journal | Journal of Pure and Applied Algebra |

Volume | 210 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 2007 |

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## Cite this

Day, B. J., & Lack, S. (2007). Limits of small functors.

*Journal of Pure and Applied Algebra*,*210*(3), 651-663. https://doi.org/10.1016/j.jpaa.2006.10.019