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Solution to Algebra Chapter 0

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This is a solution manual for Paolo Aluffi's ALGEBRA, Chapter 0, a textbook that introduces abstract algebra using the language of categories. I find this approach to be particularly appealing. So I'm enthusiastic to share my solutions to the exercises in this book for others to reference.

As a beginner, I'm trying to make my proof explict and detailed, but unfortunately it seems verbose and tedious sometimes. Anyway, I would appreciate it if you can point out my mistakes, big or small.

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