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Hello everyone, I want to ask a question but forgive me if it is so simple.

Consider the poset of natural numbers as a category, B. Verify that a subset A of B, considered as full subcategory of B, is

• reflective in B if and only if A is infinite, • coreflective in B if and only if 0 is element of A.

Thanks any advance..

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 It pays to write down a picture of B, and the inclusion of A, and also what the definition of (co)reflectivity is in this instance. That said, this question is clearly an exercise, and hence out of the scope of MO. – David Roberts May 23 2012 at 10:07
A better exercise would be to work out the characterization of reflective subcategories of linear orders (or even partial orders) in general. Then you can get the coreflective case by duality. – Andreas Blass May 23 2012 at 13:27

closed as off topic by David Roberts, Steven Landsburg, Benjamin Steinberg, Andreas Blass, MTS May 23 2012 at 17:13

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