Re: Confused about Cartesian closed categories

I am afraid that different authors make different asssumptions. I guess the minimum you want is finite products (except that a C-monoid is sometimes defined as a CCC with one object, so it has only finite non-empty products), while others will want finite limits. They are definitely different, no doubt of that and the complexity of the computations in the initial CCC of those types is different too, so the difference is important. There is an open question of some interest: can an FP CCC with NNO be embedded into an FL CCC with NNO in a way that preserves the NNO. I conjecture that it cannot, but if it could, that would have some interesting consequences. --Michael