Core the cabbage and cut it into fine, long shreds.
Peel the carrots and grate them coarsely. Cut the green chili into thin, long strips. Heat the oil in a wide, casserole-type pot over a medium-high flame. When hot, put in the asafetida. A second later, put in the mustard seeds. As soon as the mustard seeds begin to pop, put in the dried red chili. Stir once. The chili should turn dark red in seconds. Now put in the cabbage, carrots and green chili. Turn the heat down to medium and stir the vegetables around for half a minute. Add the salt, sugar and green coriander. Stir and cook for another 5 minutes or until the vegetables are just done and retain some of their crispness. Ad the lemon juice. Stir to mix. (Remove the whole red chili before serving to those unfamiliar with Indian foods.)