It seems to me that the ["indization"](http://ncatlab.org/nlab/show/ind-object) 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](https://mathoverflow.net/a/80017/7952) 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?



Is $\text{Ind-}\bf C$ the category of models for a sketch?
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.


