Limits of small functors

Brian J. Day; Stephen Lack

doi:10.1016/j.jpaa.2006.10.019

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Limits of small functors

Brian J. Day·Stephen Lack

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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*,V]. If K is large, its free completion under colimits is the V-category PK 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 PK.

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Brian J. Day, Stephen Lack. 2006-10-13. Limits of small functors. https://doi.org/10.1016/j.jpaa.2006.10.019

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