  We consider two categories related to symplectic manifolds:
  1. Objects are symplectic manifolds and morphisms are symplectic embeddings.
  2. Objects are symplectic manifolds endowed with compatible almost complex
structure and morphisms are pseudoholomorphic maps.
  We define new homotopy theories for these categories. In particular, we give
definitions of homotopy equivalent symplectic manifolds and define new
cohomology theories. Theses cohomology theories are functorial, homotopy
invariant and have other interesting properties.
  We also construct triangulated persistence category of symplectic manifolds.
This allows to apply machinery developed Biran, Cornea, and Zhang and define
distances between symplectic manifolds.
