Thinly slice the cabbage and red onion. Shred the carrot.
Place in a large bowl.
Place the jalapeño on a cutting board and slice the stem off, then slice in half lengthwise. Remove the seeds by scraping off with a knife and discard them.
Thinly slice the jalapeño and toss into the bowl.
Add the rest of the ingredients and mix it up. Adjust the amount of lime juice, salt, and pepper to your desired taste.