Kuranishi chart categories satisfy a higher homotopical bundle-component cocycle condition automatically, replacing rigid conditions with flexible homotopy-theoretic compatibility.
Isaksen,Hypercovers and simplicial presheaves, Math
2 Pith papers cite this work. Polarity classification is still indexing.
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Defines L∞-Kuranishi spaces via L∞[1]-algebras on Kuranishi charts and proves they form a category embedding smooth manifolds, by modifying conditions from prior work.
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Kuranishi chart categories and higher cocycle conditions
Kuranishi chart categories satisfy a higher homotopical bundle-component cocycle condition automatically, replacing rigid conditions with flexible homotopy-theoretic compatibility.
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Categorical structures of Kuranishi spaces with $L_{\infty}[1]$-algebras
Defines L∞-Kuranishi spaces via L∞[1]-algebras on Kuranishi charts and proves they form a category embedding smooth manifolds, by modifying conditions from prior work.