\$$g\$$ is an element of \$$X^B\$$, i.e., it is a function from \$$B\$$ to \$$X\$$. \$$\lambda\$$ is the lambda operator from the [Lambda Calculus](https://en.wikipedia.org/wiki/Lambda_calculus) (which I know almost nothing about). So, 2), in words, says that \$$f\$$ maps to composition with \$$f\$$.

Edit: Maybe there is some way to look at composition with \$$f\$$ as what you were describing?