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<p>We develop Weiss’s manifold calculus in the setting of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-categories, where we allow the target <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-category to be any <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-category with small limits. We will establish the connection between polynomial functors, Kan extensions, and Weiss sheaves, and will classify homogeneous functors. We will also generalize Weiss and Boavida de Brito’s theorem to functors taking values in arbitrary <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-categories with small limits.</p>

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A context for manifold calculus

  • 期刊论文

  • 发表日期：

    2026年3月20日

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  • Kensuke Arakawa

摘要

We develop Weiss’s manifold calculus in the setting of \(\infty \) ∞ -categories, where we allow the target \(\infty \) ∞ -category to be any \(\infty \) ∞ -category with small limits. We will establish the connection between polynomial functors, Kan extensions, and Weiss sheaves, and will classify homogeneous functors. We will also generalize Weiss and Boavida de Brito’s theorem to functors taking values in arbitrary \(\infty \) ∞ -categories with small limits.