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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.

6 votes
1 answer
301 views

Reference request: maps between moduli spaces

I want to understand the relationship between moduli spaces as we vary the different parameters. I'll focus on the moduli space ${\mathcal M}_{g,n}(X,\beta)$ of stable maps from genus $g$ curves with …
David Spivak's user avatar
  • 8,659
2 votes
0 answers
177 views

How to characterize good "models" of a category

Let ${\bf Cat}$ denote the category of small categories. Recall that for a category $\mathcal{C}$ and a functor $F\colon\mathcal{C}\to{\bf Cat}$, the Grothendieck construction of $F$, which I'll deno …
David Spivak's user avatar
  • 8,659
3 votes
1 answer
170 views

Parameter estimation using bayesian update on moduli space?

Scientists take a set of data points, say in ${\mathbb R}^2$, and, assuming that this data should fit a polynomial of degree $d$ (or an exponential, etc.), they estimate parameters. I would think tha …
David Spivak's user avatar
  • 8,659