I have heard the following "picture" mentioned in this connection. Suppose the half strip you have mentioned is a wide street heading off to infinity, and you are driving a car along it. Suppose the modulus of the Riemann zeta function is like a ceiling above you. Then, whatever smooth shape you imagine for a portion of this ceiling, you will eventually see it on the way(of course, with prescribed accuracy).

In fact I do not know how to make it more readable. If someone knows, please feel free to suggest, or if he/she has enough reputation, edit it himself/herself.

Yes that is true. I had asked this question in 3 pieces elsewhere and failed to get an answer. When I posed it here I just glued up the pieces out of laziness, without much editing. That's why. :)

Yes, Webster is right. Anweshi gave the citation of GIT, which uses schemes in its definition.

So please reopen it for 2-3 days and see what happens. I suppose you have nothing much to lose by that. You can always close it later. Is it not fair enough? In an hour or so, already 4 positive votes came for the question.

There is a saying, "there are more noncommutative geometry theories than there are noncommutative geometers". This had the potential to generate a lot of interesting answers. You should have let some more answers come, before hastily closing it. See the answers and then decide whether this was a real question or not. Let noncommutative geometers answer. This is the hottest question in that subject, I would say.

The other question was styled like being asked by a beginner in category theory. This one is asked by a person who used bits and pieces of categories, but is dissatisfied with what he learned as foundational justifications, when faced with the next level of the usage, for example usage in functorial algebraic geometry. There is a difference between the two. Well, a few answers to this question might have appeared as answers to that earlier question

@Ilya. I suppose, in your sense, the following would be a proof sketch of Riemann mapping theorem... :D just joking .. .. Once there, you have either the whole plane or you're inside the complement of a ray. In the latter case, you are between a disk and a disk, so there's some approximation thing that says you're also a disk.

Thanks!! :D Do I not have a proper claim towards the best answer?

For the definition of coarse and fine moduli spaces, I follow what is given in Mumford's Geometric Invariant Theory. A moduli problem, if you want, is the functor you are seeking to represent, in the context of definitions in that book. I suppose this book is quite standard. No??

The examples of category of all categories, category of all functors, Yoneda embedding, etc, I have mentioned, does not make sense within either the Zermelo-Fraenkel, or Godel-Bernays set theories, which are the ones mentioned in the book I have referred to. I am sorry; I wanted the question to be short; so I gave the book reference and gave examples without detailed arguments of why they don't work out. But it is really easy to see, if you just look at the definitions, etc.

Yes it could be considered potentially offensive. I have edited.

See R. Narasimhan, Several Complex Variables, published as part of Chicago Lectures in Mathematics. It is quite a small book and discusses precisely the most important topics.