# Derived coisotropic structures II: stacks and quantization

## TL;DR

This paper extends the theory of shifted coisotropic structures to derived stacks, establishing their properties, equivalences with Lagrangian structures, and existence of quantizations for certain shifts.

## Contribution

It generalizes coisotropic structures to derived stacks, compares them with shifted Lagrangian structures, and proves the existence of their quantizations for shifts greater than one.

## Key findings

- Intersection of coisotropic morphisms has a shifted Poisson structure
- Non-degenerate coisotropic and Lagrangian structures are equivalent
- Quantizations exist for n-shifted coisotropic structures when n>1

## Abstract

We extend results about $n$-shifted coisotropic structures from part I of this work to the setting of derived Artin stacks. We show that an intersection of coisotropic morphisms carries a Poisson structure of shift one less. We also compare non-degenerate shifted coisotropic structures and shifted Lagrangian structures and show that there is a natural equivalence between the two spaces in agreement with the classical result. Finally, we define quantizations of $n$-shifted coisotropic structures and show that they exist for $n>1$.