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Dec 19, 2012 at 0:41 comment added Tom Leinster Yes, I agree, and I see why you mentioned it in response to the original question. It's just that when I saw your answer, I thought to myself: "what is this category?" It took me a little time (pleasant enough) to figure it out, so I thought I'd leave a comment to help anyone else who was puzzled by where your example came from. Sorry if my comment sounded dismissive.
Dec 18, 2012 at 15:40 comment added juan @Tom Leinster It is my attempt to give a sense the question of the OP. Presented as I have done it, you may insert this category under Peano axioms of Natural Numbers (as formulated for example in E. Mendelson, Introduction to Mathematical Logic, van Nostrand 1964). In this way you may think that it is part of a theory previous to Set Theory.
Dec 18, 2012 at 12:40 comment added Tom Leinster To demystify this category: it's equivalent to the category of finite cyclic groups.
Dec 17, 2012 at 17:50 history answered juan CC BY-SA 3.0