Theorem. [dt-002Y]

The two functor laws follow as a consequence of the universal property for functions:

1. \mathsf {id}_A \twoheadrightarrow \mathsf {id}_B = \mathsf {id}_{A \twoheadrightarrow B}
2. (f \circ g) \twoheadrightarrow (h \circ i) = (g \twoheadrightarrow h) \circ (f \twoheadrightarrow i)