Church and Farb in [@CF] to provide a language for dealing with families of algebraic objects which were somehow consistently acted on by the symmetric groups. More precisely, let $\{X_n\}_{n \in {\mathbb{N}}}$ be a family of modules over a fixed commutative ring $k$ such that,

1.  for every injection of sets $f:[m] \rightarrow [n]$ there is a map $f_{\text{*}}:X_m \rightarrow X_n$;

2.  if $f,g$ are two composable injections then $(f\circ g)_{\text{*}}= f_{\text{*}}\circ g_{\text{*}}$;

3.  there is a finite set $\{v_i\} \subseteq \bigoplus_n X_n$ such that for all $n$, every element $v \in X_n$ can be expressed as $v = \sum_{i} a_i(f_i)_{\text{*}}(v_i)$, where $f_i$ is some injection of sets, and $a_i \in k$.\

Then we say that the family $\{X_n\}$ is **representation stable**. For instance, configuration spaces $\operatorname{Conf}_n(Y)$ admit forgetful maps on their points, which, in turn, induce maps on their cohomology groups $f_{\text{*}}: H^i(\operatorname{Conf}_m(Y)) \rightarrow H^i(\operatorname{Conf}_n(Y))$ for every injection of sets $f:[m] \hookrightarrow [n]$. It was proven by Church [@Chu Theorem 1], and later reproven by Church, Ellenberg and Farb [@CEF 6.2.1], that the collection $H^i(\operatorname{Conf}_{\bullet}(Y))$ is representation stable, assuming $Y$ is an orientable manifold of dimension at least 2. Since then, there has been a tremendous boom of asymptotically 