Shifted Coisotropic Correspondences

Abstract

We define (iterated) coisotropic correspondences between derived Poisson stacks, and construct symmetric monoidal higher categories of derived Poisson stacks where the $i$-morphisms are given by $i$-fold coisotropic correspondences. Assuming an expected equivalence of different models of higher Morita categories, we prove that all derived Poisson stacks are fully dualizable, and so determine framed extended TQFTs by the Cobordism Hypothesis. Along the way we also prove that the higher Morita category of $E_n$-algebras with respect to coproducts is equivalent to the higher category of iterated cospans.

arXiv comment51 pages, v2: accepted version

References in corpus (13)

• Enriched $\infty$-categories via non-symmetric $\infty$-operads
• Shifted Poisson Structures and Deformation Quantization
• Iterated spans and classical topological field theories
• On the Unicity of the Homotopy Theory of Higher Categories
• The higher Morita category of $E_n$-algebras
• Derived coisotropic structures II: stacks and quantization
• Derived coisotropic structures I: affine case
• Shifted Poisson and symplectic structures on derived N-stacks
• Braces and Poisson additivity
• Quantisation of derived Lagrangians
• Duals and adjoints in higher Morita categories
• On the fibrewise effective Burnside $\infty$-category
• Symplectic and Poisson derived geometry and deformation quantization

Cited by in corpus (7)

• Free algebras through Day convolution
• Higher semiadditive Grothendieck-Witt theory and the $K(1)$-local sphere
• On (co)ends in $\infty$-categories
• Shifted coisotropic structures for differentiable stacks
• On the Farrell-Jones conjecture for localising invariants
• A monoidal Grothendieck construction for $\infty$-categories
• Lagrangian Relations and Quantum $L_{\infty }$ Algebras