Let \(\mathcal{J}\) be a category presented by the finite graph \((\{v_1,...,v_n\},A,s,t)\) with some equations.
Let \(\mathcal{J}\xrightarrow{D}\mathbf{Set}\) be some set-valued functor.
The set \(\underset{\mathcal{J}}{lim}D := \{(d_1,...,d_n)\ |\ \forall i: d_i \in D(v_i)\ \text{and}\ \forall v_i\xrightarrow{a}v_j \in A: D(a)(d_i)=d_j\}\)
... together with projection maps \(lim_\mathcal{J}D \xrightarrow{p_i}D(v_i)\) given by \(p_i(d_1,...,d_n):=d_i\)
... is a limit of \(D\). NOCARD
NOT PROVEN