Complete categories are cocomplete? I've read in a paper and on wikipedia that any (small) category is complete if and only if it is cocomplete. 
Now obviously if one shows that complete$\implies$cocomplete, then it's easy to conclude from there, but I have no idea why that would be true. 
Could anyone care to explain it to me ?

The partial ordered class of sets has all suprema, but not all infima, since it lacks a largest element. Hence, its dual category is complete and not cocomplete.
