As it is stated in the definition here : https://en.wikipedia.org/wiki/Deligne%E2%80%93Mumford_stack , a Deligne-Mumford stack needs to verify the following axiom :
A Deligne–Mumford stack is a stack $ F $ such that :
- The diagonal morphism $ \displaystyle F \to F\times F$ is representable, quasi-compact and separated.
Could you explain to me why ?
Thanks for the help.