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\$$.