In Lurie's Higher Topos Theory Proposition A.3.2.4, the author used Proposition A.2.6.15 to prove that for any combinatorial monoidal model category $\mathbf{S}$
with all objects cofibrant and weak equivalences stable under filtered colimits, the category $\mathbf{Cat\_S}$ is a left proper combinatorial model ctegory, where he implicitly used the statement:



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> $\mathbf{Cat\_S}$ is locally presentable.
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Why is this statement true? Can anybody give me some help? Thanks in advance!



Why is the category of all small $\mathbf{S}$-enriched categories locally presentable?
This is proved in the paper



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> Kelly, G. M.; Lack, Stephen. $\scr V$-Cat is locally presentable or locally bounded if $\scr V$ is so. *Theory Appl. Categ.* 8 (2001), 555--575. <http://tac.mta.ca/tac/volumes/8/n23/8-23abs.html>
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as an instance of the fact (proved by Gabriel and Ulmer) that the category of algebras for a finitary monad on a locally $\lambda$-presentable category is locally $\lambda$-presentable (for $\lambda$ a regular cardinal). 


To wit, Kelly and Lack show that if $\scr V$ is a [monoidally cocomplete category](https://ncatlab.org/nlab/show/monoidally+cocomplete+category), then the category ${\scr V}\textbf{-Cat}$ of $\scr V$-enriched categories is finitarily monadic over the category ${\scr V}\textbf{-Gph}$ of $\scr V$-enriched graphs, which they show to be locally $\lambda$-presentable if $\scr V$ is so. (Note that, by definition, a combinatorial monoidal model category is in particular monoidally cocomplete and locally presentable.)


