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 ?

This is not true in general for a given category $C$. On the other hand, note that $\mathbf{Set}^{C^{op}}$, $is$ complete and cocomplete, and that the Yoneda Lemma provides an embedding $\ y \colon C \rightarrow \mathbf{Set}^{C^{op}}. $  That is,  $C$ can be "enlarged" to a category that is complete and cocomplete. 
