Is there a standard reference for the theory (if it exists) of $\mathcal{V}$-enriched locally presentable categories? Here $\mathcal{V}$ is a cosmos. Does anything unexpected happens here in contrast to the case $\mathcal{V}=\text{Set}$ treated in "Locally Presentable And Accessible Categories" by Adamek & Rosicky? In particular I'm interested in the case $\mathcal{V} = \text{Cat}$. 



Enriched locally presentable categories
The standard reference is Max Kelly’s 1982 paper [“Structures defined by finite limits in the enriched setting”](http://archive.numdam.org/ARCHIVE/CTGDC/CTGDC_1982__23_1/CTGDC_1982__23_1_3_0/CTGDC_1982__23_1_3_0.pdf).


Perhaps the most unexpected thing is how well the theory works!


