Example 8.1:

We see that the family of all groups ${\bf Gr}$ forms a category where Mor$(G, H)$ consists of the set of all group homomorphisms from $G$ to $H$.

(ii) Likewise we can look at the family ${\bf AbGr}$ of all abelian groups and as before Mor$(G, H)$ consists of all group homomorphisms from $G$ to $H$.

(iii) The class of all topological spaces Top forms a category if we take as morphisms between $X$ and $Y$ the set of all continuous functions from $X$ to $Y$.