My coworker keeps reporting my mistakes to my manager?

I started a new position and my supervisor called a meeting with me to discuss mistakes I’ve made that she found out about from my co-worker (who I'm working with). My co-worker has also sent out emails cc'ing our supervisor and head of our company outlining my mistakes. They are minor mistakes (using a semicolon) and I take full responsibility for them, but what should I say to my co-worker and supervisor?
My coworker keeps reporting my mistakes to my manager?
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