How is a morphism different from a function How is a morphism (from category theory) different from a function?
Intuitive explanation + maths would be great

If $G$ is a group, there is a famous example that constructs a category in which morphisms are not functions: you take it to consist of a single object called "$\bullet$" and state that the morphisms (of $\bullet$ to $\bullet$, because there is no other object available) are the elements of $G$. Check for yourself that all the properties defining a category are verified by this (admittedly strange) example.
