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Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.

3 votes

Help motivating log-structures

I believe that people refer to $\alpha$ as the exponential map exactly because of the "big example (I)" in Pottharst's notes. Also, a small point, for any scheme we can give many log structures. For i …
3 votes

What is a good introductory text for moduli theory?

I have read most of Newstead this term. It is easy to read, barely mentioning schemes, and introducing moduli through basic examples of classifying endomorphisms of a finite-dimensional vector space. …