A Context for Manifold Calculus

Abstract

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.

Fixed typos. Identical to the journal version except for a few editorial changes

References in corpus (7)

• Embeddings from the point of view of immersion theory: Part I
• Embeddings from the point of view of immersion theory: Part II
• Factorization homology of topological manifolds
• Semi-simplicial spaces
• Context-free manifold calculus and the Fulton-MacPherson Operad
• The universality of the Rezk nerve
• Polynomial functors in manifold calculus