Symplectic Microgeometry III: Monoids

Abstract

We show that the category of Poisson manifolds and Poisson maps, the category of symplectic microgroupoids and lagrangian submicrogroupoids (as morphisms), and the category of monoids and monoid morphisms in the microsymplectic category are equivalent symmetric monoidal categories.

19 pages, 2 figures

References in corpus (3)

• The deformation quantizations of the hyperbolic plane
• Integrating Poisson manifolds via stacks
• The Symplectization Functor

Cited by in corpus (7)

• "Nonlinear pullbacks" of functions and $L_{\infty }$-morphisms for homotopy Poisson structures
• Relational symplectic groupoids and Poisson sigma models with boundary
• Microformal geometry and homotopy algebras
• Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization
• Quantizations of Momentum Maps and G-Systems
• Symplectic Microgeometry IV: Quantization
• G-Systems and Deformation of G-Actions On Rd