Greece!

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Across
  1. 3. a race and a battle
  2. 6. a peninsula and some wars
  3. 7. you scratch my back, I'll scratch yours
  4. 8. Greek money
  5. 9. Athena temple
  6. 11. taught by questioning
  7. 12. Delphi prognosticator
  8. 13. great Athenian leader
Down
  1. 1. noble 300
  2. 2. Taylor Swift predecessor
  3. 4. he's pretty great
  4. 5. Mount Olympus FedEx
  5. 9. Greek army's winning formation
  6. 10. five-ring athletics festival