A simplicial set $X$ is a functor $\Delta^{\text{op}}\to \text{Sets}$, where $\Delta$ is the category whose objects are linearly ordered and morphisms are non-decreasing maps.

The Gelfand-Kirillov Dimension of a right module $M$ over a $k$-algebra $A$ is $$ \operatorname{GKdim} = \sup_{V, M_0} \limsup_{n\to\infty} \log_n \dim_k M_0 V^n $$

where the supremum is taken over all finite-dimensional subspaces $V\subset A$ and $M_0\subset M$.