How could I prove that two categories are not equivalent? Or how could I prove that there is no functor between two categories with certain property?
I can't imagine a way to make a proof for negative property in category... What am I missing?
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$\begingroup$ Categories have lots of invariants. For example, whether various types of limits or colimits exist in them. The homotopy type of their nerves... $\endgroup$– Qiaochu YuanCommented Aug 1, 2011 at 20:10
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$\begingroup$ Give us an example of what you want to do. But in general it's about invariants, as Qiaochu says. $\endgroup$– Andrej BauerCommented Aug 1, 2011 at 20:25
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$\begingroup$ How could I prove that two type systems are of different expressive power, using just category theory? Probably the easiest example would be of untyped and simply typed lambda calculus. $\endgroup$– Strahinja PopovicCommented Aug 1, 2011 at 20:31
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$\begingroup$ Another technique is to show that the automorphism group of an object in a category isn't isomorphic to the automorphism group of any object in the other category. $\endgroup$– Ryan BudneyCommented Aug 2, 2011 at 17:42
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$\begingroup$ Strahinja, I'm voting to close. It sounds as if you're just getting to grips with the basic ideas of category theory, which is an excellent thing to be doing, but probably means that it would be more appropriate to post your questions at math.stackexchange.com. (They'd also probably appreciate it if your questions were more focused than this one. Specific questions are good.) $\endgroup$– Tom LeinsterCommented Aug 5, 2011 at 22:54
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