# Contiguity for simplicial maps between simplicial sets

I begin by recalling the definition of contiguous simplicial maps between abstract simplicial complexes:

Definition. Two simplicial maps $$\varphi,\psi\colon K \to L$$ are said to be contiguous if for every simplex $$\sigma \in K$$, $$\varphi(\sigma) \cup \psi(\sigma)$$ is a simplex of $$L$$.

Now I wonder whether this notion has been extended for more general contexts such as simplicial sets or $$\Delta$$-complexes.

Question. Has it been studied a notion of contiguity for simplicial maps between simplicial sets (or $$\Delta$$-complexes)? If that is the case could you provide me a reference.

The exact references are Definition 1.2 and Definition 1.7. One should beware of a typo in the definition 1.2, where f,g are said to be adjacent if the set $$\{f(x)|x \in \sigma, x \leq x'\} \cup \{g(x)|x \in \sigma, x \leq x'\}$$. The correct definition should be
Definition: Two simplicial maps $$f,g:X \rightarrow Y$$ between ordered simplicial complexes $$X,Y$$ are said to be adjacent if for any simplex $$\sigma$$ and any $$x' \in \sigma$$, the set $$\{f(x)|x \in \sigma, x \leq x'\} \cup \{g(x)|x \in \sigma, x' \leq x\}$$ is a simplex in Y.