Simplicial sets can be specified using generators and relations, in complete analogy with groups, rings, etc.

More precisely, a system of generators of relations for a simplicial set
consists of a set G of generating simplices equipped with a dimension function dim: G→**N**
and a set R of relations between simplices,
equipped with a function F that sends a relation r∈R
to the tuple F(r)=(g_1(r),f_1(r),g_2(r),f_2(r)),
where g_i(r)∈G and f_i(r):[m(r)]→[dim g_i(r)] is a map of simplices of indicated dimension.

Intuitively, each element g∈G yields a simplex of dimension dim(g), and for any r∈R the generalized face of the simplex g_1(r) corresponding to the map of simplices f_1(r) must be equal to the generalized face of g_2(r) corresponding to f_2(r).

The simplicial set generated by (G,R) is the initial object in the category of pairs (X,u), where X is a simplicial set and u is a function from G to the set of simplices of X (of any dimension) such that u(g) is a simplex of dimension dim(g) and for any relation r∈R with F(r)=(g_1(r),f_1(r),g_2(r),f_2(r)) we have X_{f_1(r)}(g_1(r)) = X_{f_2(r)}(g_2(r)), which formalizes the above intuitive description.

This allows one to specify various elementary simplicial sets very efficiently. For instance, the real projective plane can be specified as a single 2-simplex α that satisfies two relations d_0(α)=d_2(α) and d_1(α)=s_0(d_1(d_1(α))).

**Are there any citeable sources that discuss this in more detail than 1-2 lines of text?**
For the purposes of this question, “citeable” means indexed by MathSciNet/zbMATH or published on arXiv.

I prefer expository sources with examples akin to the one given above,
but so far I am not aware of **any** sources that treat this in any nontrivial detail, e.g., more than a simple formula with a pushout or coequalizer.

I want to specifically emphasize that I am **not** interested in sources that
use simplicial complexes instead of simplicial sets.
(The above example makes no sense for simplicial complexes.)