In the context of global equivariant homotopy theory and global equivariant stable homotopy theory one considers equivariant spectra with equivariance not necessarily with respect to one fixed group, but with respect to a suitable family of groups at once. These “suitable families of groups for defining global equivariant (stable) homotopy theory” are called global families, for short.

A global family is said to be reflexive if and only if the inclusion into the category of all compact Lie groups has a left adjoint. Schwede 18, def 4.5.7.