I am reading The unbearable lightness of deformation theory by Balázs Szendrői.
At page 9 he defines the deformation functor associated to a dgla $\Gamma$ as $$Def_\Gamma:Art_k\longrightarrow Sets,$$ where $Art_k$ is the category of local artinian rings over $k$ and $Sets$ is the category of sets, sending $R=k\oplus m$ (i.e. $m$ is the maximal ideal of $R$) to $$MC(\Gamma\otimes m)/(\text{gauges}).$$ Later on we can read:
Remark 3.4 By a reasonably standard result of Schlessinger, the functor defined above is pro-represented by a complete local $k$-algebra $R_\Gamma$ in the sense that the functors $Def_\Gamma$ and $\hom_{k-alg}(R_\Gamma,-)$ from $Art_k$ to $Sets$ are isomorphic.
Does anyone have a reference for this result, or at least a precise statement (i.e.: how can one construct $R_\Gamma$?)
See the proof of Theorem 2.11 in http://www.math.harvard.edu/~amathew/schlessingerdef.pdf you could have easily found this via Google...