groupoid of finite sets.

Question

I'm newbie to the category and groupoid, and I got confused about the definition of groupoids.

In the definition of groupoid in the Wikipedia, it says a groupoid is a "small" category such that every morphism is isomorphism.

And I'm sure I'm wrong, but I don't know why the finite sets with bijections form a groupoid (this may not be true, and if i'm not correct, please correct me), since the class of finite sets is not a set, which is a requirement to be a small category.

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http://mathoverflow.net/questions/1114/whats-a-groupoid-whats-a-good-example-of-a-groupoid — isomorphismes, Apr 13 '15 at 08:47

score 0 · Accepted Answer · answered Nov 08 '14 at 19:56

There's no reason to restrict attention to small groupoids. A groupoid should just be a category such that every morphism is an isomorphism. In any case, the groupoid of finite sets and bijections is essentially small, meaning that it's equivalent to a small groupoid, and that's usually good enough.

groupoid of finite sets.

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