Limits of small functors (Q886254)

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