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  1. #1
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    Let C be a category with  Obj(C) = \mathbb{Z}^+ and for two positive integers  a and  b, there is exactly one morphism  a \rightarrow b iff  a divides b without remainder, and  Hom(a,b) = \emptyset otherwise. In this category, verify that there are products and coproducts. What are they?

    My question - I've worked through it, and I came up with the products being the greatest common divisor of two integers and the coproducts the least common multiple. I just wanted to make sure I had come up with the correct interpretation before moving on.
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  2. #2
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    Quote Originally Posted by Math Major View Post
    Let C be a category with  Obj(C) = \mathbb{Z}^+ and for two positive integers  a and  b, there is exactly one morphism  a \rightarrow b iff  a divides b without remainder, and  Hom(a,b) = \emptyset otherwise. In this category, verify that there are products and coproducts. What are they?

    My question - I've worked through it, and I came up with the products being the greatest common divisor of two integers and the coproducts the least common multiple. I just wanted to make sure I had come up with the correct interpretation before moving on.
    yes, it is correct.
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