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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.
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Stable cohomology of mapping class group with coefficients in $H^{\otimes n}$
Appendix B of Randal-Williams' "Cohomology of automorphism groups of free groups with twisted coefficients" gives a stable description of the graded $\mathbb{Q}[\Sigma_q]$-module $H^*(\Gamma_g;H^{\oti …