Shifted Coisotropic Correspondences

TL;DR

This paper develops a higher categorical framework for derived Poisson stacks using coisotropic correspondences, proving their full dualizability and implications for topological quantum field theories.

Contribution

It introduces a new higher categorical structure for derived Poisson stacks and establishes their full dualizability, connecting to the Cobordism Hypothesis.

Findings

Derived Poisson stacks are fully dualizable.

Higher Morita categories of $E_{n}$-algebras are equivalent to iterated cospans.

Constructs symmetric monoidal higher categories of 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.