A concrete category is a category C together with a function that assigns to each object A of C a set called the underlying set of A.
Example: The category of groups, equipped with the function that assigns to each group its underlying set in the usual sense, is a concrete category.
What is the underlying set for an object in a category of groups ?
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3$\begingroup$ As far as I can tell you answered your own question just before you asked it. $\endgroup$– Jonas MeyerAug 9, 2010 at 19:33
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$\begingroup$ This question is probably better suited to math.stackexchange.com - mathoverflow is intended for “research level” questions, whereas this is more like an exercise for a first course in category theory. $\endgroup$– Peter LeFanu LumsdaineAug 9, 2010 at 19:34
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1$\begingroup$ You don't want a function, but a functor, and it has to be faithful. $\endgroup$– Qiaochu YuanAug 9, 2010 at 19:39
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1 Answer
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The underlying set for an object in the category of groups is just the underlying set of the group, there is no other name for it.