Left quotient of a formal language ($u^{-1}L$)

For a word $u$ and a formal language $L$, the left quotient $u^{-1}L=\{w:uw\in L\}$ is the possible continuation language after the prefix $u$. Two prefixes have the same left quotient exactly when they are Myhill-Nerode equivalent. For a regular language only finitely many distinct left quotients occur.