Hello categorists To those who have replied on my question and others. First i want to thank for the suggestions of problems. Since i am new here some people assume that i seek a problem to solve so i can quickly become famous. I am in fact much more interested in the structure and foundation of mathematics than solving math problems. I just felt i should know these problems since they are famous, but almost none came to mind. A reason for this is that the proofs i have seen have mostly been "not water tight", they miss some things (mostly in the logic). And, they are not spelled out in full but are very "cut down" in their arguments. This makes them too time consuming to follow. I don't want to read a proof to recreate half of it but to understand why something is true. "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street" -David Hilbert I argue that the same is true for proofs. Something to think about next time you write a proof. In Dyson Freemans terminology i am a bird and not a frog. As a bird i must say that it is sad that about 90% of mathematicians are frogs. This give an inbalance in mathematics. To answer Michael Shulman: Yes, there is something different about category theory. It is at the top of mathematics. A perfect place for a bird :) Now to my question. After some intensive work and help from people on the mailing list i have found some problems that are interesting in ordinary category theory :) You just have to learn to see them. Some won't be stated even as problems to solve. To illustrate my point: How many categories of n objects are there up to categorical equivalence for n a natural number? If it can not be given directly, can it be expressed by other counting functions? Maby the pattern is easier than that for groups. A simplified version of the problem is to count only finite categories with at most 1 morphism between any objects. This suggests the NC(r,s)-problem: What is the number of categories with r objects and at most s morphisms (in one direction) between any two objects. Specialized versions of these are to count model categories, toposes (defined as categories and not as 2-categories),... Correct me if it is not so, but i don't know of any theorem that model categories or toposes must be infinite. Another example first stated by John Baez that i call the no-go quantization conjecture: There is no functor from the symplectic category (symplectic manifolds and symplectomorphisms) to the Hilbert category (Hilbert spaces and unitary operators) that preserves positivity. I.e. a one-parameter group of symplectic transformations generated by a positive Hamiltonian is mapped to a one-parameter group of unitary operators with a positive generator. That maby helps to find the problems. Not that i am trying to popularize them. If you know some you can still e-mail them to me. Now from the question to the mysterious Hasse Riemann! It seems that people wonder about me so here i go. This is written from a 15 year old gymnasium account from the time of the beginning of internet. Bernhard Riemann was my hero then because of riemannian geometry and riemann surfaces. Actually i have still not managed to replace Riemann! Hasse is just a name that i think fits me more than Rafael. Since everyone i e-mail knows me by this pseudo i have decided not to change it. It took me 20 years of studying mathematics to find category theory. It is a long time but it was hardly wasted time. I actually went into category theory 3 times before (not so deep), but not until this fourth time i understood what category theory really is and that it is precisely what i was looking for :) ,and hence decided to stay here for a long while. The first year in category theory went with a blazing speed. Now, a half year after that i have more questions than facts. I happen to be seated in Stockholm. It is not a bad place but there are no category theorists in Sweden! Hence i'm counting on you people. Best regards Rafael Borowiecki [For admin and other information see: http://www.mta.ca/~cat-dist/ ]