What does Hanukkah celebrate or remember?

The Jewish Festival of Lights is Hanukkah and it honors the rededication in Israel of the second Jewish Temple in Jerusalem. In the 160s BCE/BCC, this occurred (before Jesus was born).

In the second century B.C., the eight-day Jewish festival celebrated as Hanukkah or Chanukah commemorates the rededication. The Second Temple in Jerusalem, where according to tradition, in the Maccabean rebellion, Jews stood up against their Greek-Syrian oppressors.

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no questions on whether they are allowed that right