We describe the modular operad structure on the moduli spaces of pointed stable curves equipped with an admissible -cover. To do this we are forced to introduce the notion of an operad colored not by a set but by the objects of a category. This construction interpolates in a sense between “framed” and “colored” versions of operads; we hope that it will be of independent interest. An algebra over the cohomology of this operad is the same thing as a -equivariant CohFT, as defined by Jarvis, Kaufmann and Kimura. We prove that the (orbifold) Gromov–Witten invariants of global quotients give examples of -CohFTs.
Dan Petersen. "The operad structure of admissible $G$-covers." Algebra Number Theory 7 (8) 1953 - 1975, 2013. https://doi.org/10.2140/ant.2013.7.1953