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We demonstrate that Joyal's category Theta_n, which is central to numerous definitions of (infinity,n)-categories, naturally encodes the homotopy type of configuration spaces of marked points in R^n.
The braid groups
R. Fox and L. Neuwirth · 1962
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Graeme Segal · 1974
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Operads, homotopy algebra and iterated integrals for double loop spaces
E. Getzler and J. D. S. Jones · 1994
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