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added (locally-presentable-categories) tag - the question has been bumped anyway
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Martin Sleziak
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Martin Brandenburg
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Enriched locally presentable categories

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 $\mathcal{V} = \text{Cat}$.