in symplectic geometry will explore situations in fullest generality and examine the new phenomena not accessible in semipositive cases, and will not let the scare of virtual theories get in the way of finding out reality of symplectic geometry.

**Acknowledgement:** I am extremely grateful to Helmut Hofer for his enthusiasm and insights in math, his suggestion of PFH as a project and vision of existence of forgetful functor, numerous helpful discussions and suggestions, and supports. I am indebted to Kaoru Ono for helpful discussions, in particular informing me of Kawasaki’s groupoid construction via the frame bundle from a Satake orbifold representative and explaining to me their several gluing constructions among various topics, and his kind invitation to RIMS. I am grateful to Alexandru Oancea for his kindness, encouragement, discussions and, during exchanges and seminars, conceptual remarks. I am thankful to Bohui Chen for the invitation to lecturing on polyfolds and the opportunity to give a talk from which the current article originates and for his explanation of their gluing construction. I am appreciative of Dominic Joyce’s insights in email exchanges, helpful discussion on a category of Kuranishi structures (not R-equivalence classes), and sharing preprint [@2CAT] after I sent him the 