This talk is a report on joint work in progress with Chris
Brav. We introduce the concept of a Calabi-Yau functor between
smooth differential graded categories. Such a structure on the zero
functor $0 \rightarrow B$ recovers Ginzburg's notion of a Calabi-Yau category.
Various features of the resulting theory will be discussed, focussing
on the relationship with shifted symplectic and Lagrangian structures
when passing to moduli of objects.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/6356