Famous unsolved problems in ordinary category theory‏

Famous unsolved problems in ordinary category theory‏

[Hasse Riemann]

 
Hi categorists
 
OK, here is the beuty of collecting and spreading problems that many seem to miss.
It just took me a few days to change my mood from the depressing answers
not to look for problems. Again i am much more for structuring of mathematics.
 
Usually you only get to know what is proved and not what is unproved.
Problems complete this by letting you know what to not to look for.
They also answer your questions even if it is by saying unkown or a conjecture.
Then, on the other hand, they are good research projects so they should be widely known.
Just maby someone undertakest them and happens to find the solution.
But often he must first see the problem.
 
The problems Ross Street put forward are so beautiful i have decided to post 2 problems
i have learned from him, unedited.
 
1)
Fermat's Last Theorem is about the category of finite sets. Is there a categorical proof?
Can we characterize those categories C in which x^n + y^n isomorphic to z^n has only trivial
solutions for n> 2?
 
2)
The category of finite sets is a concrete form of the set N of natural numbers.
What are concrete forms of Z, Q, R and C?

If anyone know some problems of these sort below let me know.
 
* characterization problems
* inherit properties problems
* every category/functor/... of type A is a category/functor/... of type B
 
 
I also foregot to mention before that i know and more than like Grothendiecks philosophy
of dissolving problems by developing a proper framework for rhem.
 
Best regards
Rafael Borowiecki


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