Notes on $n$-Transformations by Theories ($n\in {\mathbb{N}^*}$)
  Clemens Berger showed that Weak Omega Categories of Michael Batanin can be defined as model of a certain kind of theories that he called "homogeneous theories". By using the work of Mark Weber on the Abstract Nerves for the specific case of the $n$-Transformations ($n\in {\mathbb{N}^*}$), we show that we can also define Weak Omega Functors, Weak Omega Natural Transformations, and so on, as models of certain kind of colored theories which are homogeneous as well. 
Camell Kachour
math.CT