TITLE: Example of a functor that doesn't reflect isomorphism
QUESTION [14 upvotes]: I'm reading the text Category theory in context from Emily Riehl, and having trouble to find an example asked on exercise $1.3.viii.$: prove that functors not need to reflect isomorphisms, i.e., find a functor $F:C\rightarrow D$ and a morphism $f$ in $C$ so that $Ff$ is an isomorphism in $D$ but is not an isomorphism in $C$.
I know that a non conservative functor from $Top$ to $Set$ might work but can't find the adequate morphism.
Any suggestion is apreciated.

REPLY [11 votes]: Homology and homotopy functors are very natural examples of this.