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It would be useful to a beginner of category theory to see some examples of adjoint pairs which are not equivalences, and which are not forgetful/inclusion types. Of course, a first is the standard Hom-tensor duality.

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 I think this belongs on math.stackexchange.com, it's not a research-level question. – Adam Hughes May 3 2011 at 22:32
Agreed. Questions like these were allowed in the early days, but now math.stackexchange.com is definitely a better place for them. For example, there is the following related question there: math.stackexchange.com/questions/25455/… – Qiaochu Yuan May 3 2011 at 22:41
Isn't the adjuntion $\otimes$-Hom interesting enough? here by Hom I mean inner hom of the category. – 36min May 3 2011 at 23:11
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 I also think that a natural place to look for examples of adjunctions might be, perhaps, the chapter of Mac Lane's CWM on adjunctions... – Yemon Choi May 3 2011 at 23:15
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 Not so clear what does or does not qualify as a forgetful functor... – Todd Trimble May 3 2011 at 23:38

closed as too localized by Qiaochu Yuan, David Roberts, Daniel Moskovich, Zev Chonoles, Pete L. Clark May 4 2011 at 2:23

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