Fix a field $K$ and consider a finite directed graph $\Gamma$ where multiple edges between a pair of vertices are allowed so long as the total number of edges is finite. Associate to each vertex $v$ a finite-dimensional $K$-vector space $K_v$, and to each edge $(u,v)$ a linear map $f_{uv}:K_u \to K_v$. There is no commutativity requirement on the composition along different paths between the same two vertices. Those familiar with representation theory will immediately recognize this as a (nice and finite) *quiver representation*.

Now, $\Gamma$ may also be interpreted as a finite diagram in the category of vector spaces with linear maps as morphisms and as such, it has a (co)limit. Here is my question:

Is there software which takes such a finite quiver representation $\Gamma$ as input and computes a basis for $\lim(\Gamma)$ as a vector space along with all the matrices $\lim(\Gamma) \to K_v$ expressed in that basis for each vertex $v$ of $\Gamma$? And similarly, is there software to compute a basis for $\text{colim}(\Gamma)$ along with the matrices $v \to \text{colim}(\Gamma)$?

In principle everything is finite-dimensional linear algebra: the computations should be tractable and I'm hoping someone has written and tested this already. The types of $\Gamma$s that I'm be most interested in are zig-zags, $$ \Gamma = v_1 \leftarrow v_2 \to v_3 \leftarrow v_4 \to \cdots \leftarrow v_n $$ and also "claw graphs" consisting of a distinguished vertex $u$, other vertices $v_1,\ldots,v_n$ and a single edge $(u,v_k)$ for each $1 \leq k \leq n$.