Limits of small functors

For a small category image enriched over a suitable monoidal category image, the free completion of image under colimits is the presheaf category image. If image is large, its free completion under colimits is the image-category image of small presheaves on image, 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 image.