moore-tachikawa varieties: beyond duality

Abstract: we propose a generalisation of the moore-tachikawa varieties for the case in which the target category of the 2d tft is a hyperkaehler quotient. the setup requires generalising the bordism operators of moore and segal to the case involving lack of reparametrisation-invariance on the riemann surface, ultimately enabling to relate this to the issue of defining a drinfeld center for composite class s theories.