# Why is the category of all small $\mathbf{S}$-enriched categories locally presentable?

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:

$$\mathbf{Cat_S}$$ is locally presentable.

Why is this statement true? Can anybody give me some help? Thanks in advance!

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
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, 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.)