Is $\text{Ind-}\bf C$ the category of models for a sketch? It seems to me that the "indization" process of a category can be formulated in the language of sketches (by sketch I mean what is defined in [LPAC].2.F, Def. 2.55); in particular, see this answer by T. Johnson-Freyd.
Expressing the ind-completion of $\bf C$ as the category of models for a sketch $({\bf C},\{\text{filtered categories}\}, \varnothing, \sigma)$ would be extremely useful to generalize the construction of $\text{Ind-}\bf C$ to the case of other partial free-(co)completion of $\bf C$, which add certain rescribed "shapes" of (co)limits, and leave the rest unchanged: I can easily imagine the sifted-, discrete-, connected-, empty-completion and cocompletion of $\bf C$, but I would like to fit this prcedure in a general framework. In this vein, sketches are perfect.
My question is: am I right in doing this? Caan you point me to somewhere in the literature where this is explained in full detail?
 A: Quoting the nLab article on accessible categories: 
$C$ is accessible iff one of the following equivalent conditions holds: 


*

*it is the category of models (in $\mathbf{Set}$) of some small sketch.

*it is of the form $\text{Ind}_\kappa(S)$ for $S$ small, i.e. the $\kappa$-ind-completion of a small category, for some regular cardinal $\kappa$.

*it is of the form $\kappa\,\text{Flat}(S)$ for $S$ small and some $\kappa$, i.e. the category of $\kappa$-flat functors from some small category to $\mathbf{Set}$.

*it is the category of models (in $\mathbf{Set}$) of a suitable type of logical theory. 
If you are interested in the classical filtered colimit completion, that is the case where $\kappa = \omega$. This material is covered in Locally Presentable and Accessible Categories; see specifically the chapter on accessible categories. 
A: As suggested I repost my comment as an answer.
The paper Adámek, Borceux, Lack, Rosický, A classification of accessible categories addresses exactly these types of questions. In particular, Section 3 is about the Ind construction and Section 4 is about sketches. Everything is relative to some nice class of small categories $\mathbb{D}$ and these colimits that commute with $\mathbb{D}$-limits.
