1
$\begingroup$

Suppose $f$ and $g$ are injective maps such that $h \circ f = g $. What are the requirements on $h$?

Thanks

2 Answers 2

1

Denoting by $Im(f)$ the image of the map $f$, the only requirement you need on $h$ is that $h$ is defined at least on $Im(f)$ and injective on this set.

0

Well, $h$ must be defined as $g\circ f^{-1}$ on the image of $f$. Elsewhere, it may be anything.