Martin's Blog

Group actions and universality

Posted by martin on Monday, 27 April 2009 at 13:23

This continues my earlier post on groups and actions. I want to think some more about Cayley’s theorem, and describe how it provides an example of a universal property. (With regard to James’s comment on that post, I think universality may be a better way than injectivity of describing my concept of “active group” but I’m not sure how to do that in full).

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Active and passive groups

Posted by martin on Thursday, 02 October 2008 at 19:13

I have been studying category theory recently, and revising my idea of what a group is. There are two ways of thinking about groups, which I shall call active and passive. I have tended to almost exclusively think about groups passively, but I have realised that treating groups as active is useful too.

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