Here is an example of what I mean by a connected tree:
* \\(f: A,B \rightarrow X_1\\)
* \\(g: C,D \rightarrow X_2\\)
* \\(h: X_1,X_2 \rightarrow Y\\)
It's 'connected' in the sense that the first input to \\(h\\) is fed by the output of \\(f\\), and the second input of \\(h\\) is fed by the output of \\(g\\).
The composite morphism will map \\(A,B,C,D \rightarrow Y\\).