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Higher-categorical combinatorics of configuration spaces of Euclidean space
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abstract
We examine configurations of finite subsets of manifolds within the homotopy-theoretic context of $\infty$-categories by way of stratified spaces. Through these higher categorical means, we identify the homotopy types of such configuration spaces in the case of n-dimensional Euclidean space in terms of the category $\mathbf{\Theta}_n$.
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On dualizability and invertibility in the higher Morita category
An E_n-algebra is (n+1)-dualizable in the higher Morita category exactly when it is dualizable as a module over each sphere-shaped factorization homology, confirming conjectures of Lurie and Brochier–Jordan–Safranov–Snyder.
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