A proven homological mirror symmetry for elementary birational cobordisms is expected to be generalizable to cases when
the center is nontrivial and admits a mirror. In these cases, categories are installed in similar patterns. I will share some
speculations on the existence of a structure that sees these patterns and entails the expected mirror symmetry from within.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/4234
[3] https://www.mpim-bonn.mpg.de/node/3207