Functor that does not preserve monic and epic
Hint: Let $M$ be a free monoid.
A simple example is with $M=(\Bbb N,+),\ \,N=(\{0,1\},\max)$ and $F(m)=\min(1,m)$.
$1$ is cancellable in $M$ but not in $N$.
Hint: Let $M$ be a free monoid.
A simple example is with $M=(\Bbb N,+),\ \,N=(\{0,1\},\max)$ and $F(m)=\min(1,m)$.
$1$ is cancellable in $M$ but not in $N$.