Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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 ?

share|cite|improve this question

closed as no longer relevant by Jonas Meyer, Robin Chapman, Qiaochu Yuan, Pete L. Clark, José Figueroa-O'Farrill Aug 9 '10 at 20:11

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

As far as I can tell you answered your own question just before you asked it. –  Jonas Meyer Aug 9 '10 at 19:33
This question is probably better suited to - mathoverflow is intended for “research level” questions, whereas this is more like an exercise for a first course in category theory. –  Peter LeFanu Lumsdaine Aug 9 '10 at 19:34
You don't want a function, but a functor, and it has to be faithful. –  Qiaochu Yuan Aug 9 '10 at 19:39

1 Answer 1

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.

share|cite|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.