# Locally constant constructible vs locally constant

A very short and easy question. Why do people write "locally constant constructible sheaf" (e.g. everywhere in SGA) instead of just "locally constant sheaf"? A constructible sheaf is by definition locally constant on a stratification, hence locally constant implies locally constant constructible. And locally constant constructible implies locally constant. So the two notions should be the same. Have I misread the definitions?

• Apparently "constructible" has a second meaning: mathoverflow.net/questions/69422/… – Qiaochu Yuan Feb 24 '14 at 7:40
• Indeed, if we impose finiteness in the definition of constructibility, then "locally constant constructible sheaf" is a bit shorter than "locally constant sheaf of finite groups". On the other hand, the Stacks Project seems to be using "finite locally constant", which sounds nicer. – Piotr Achinger Feb 24 '14 at 7:45
• If I recall it correctly constructible does require locally constant (with respect to a stratification) of finite rank (local system on each stratum)! – Oliver Straser Mar 26 '14 at 9:51