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How can we associate a vector space structure to a category with one object ? Is there a canonical way of doing this ?

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    A category with one object is just a group. So it's just the same as asking if you can associate a vector space to a group. And there's several ways of doing that, it depends what you're after.2011-05-22
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    @George: a _locally small_ category with one object is just a _monoid._ @Christiaan: I don't really understand the question as stated. What do you want this vector space to do?2011-05-22
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    @Qiaochu: Sorry, you're right, I should have said monoid. Still, the same comment applies. It depends what the OP is after.2011-05-22

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