coordinate system with the starting point of other approaches such as [@MW] and [@CLW] are closer. The key concepts in [@DI] are level-1 structures (\[LEVEL1CATEXIST\], which gives some immediate results in the spirit and direction of this article) and R-equivalence (\[REQUIV\], just called equivalence therein), and they will play important roles[^5] in reaching the unifying picture.

Besides learning ingredients from other virtual machineries from their originators at conferences, preparing a talk about how the polyfold theory fits with other virtual machineries gives me an opportunity to take a very quick look at other virtual machineries, and I hope to update this article, as my knowledge about details and advantages of other virtual theories grow. Therefore, along the way, any comments and criticisms are welcome. Strictly speaking, this article does not validate each approach (in the sense of they having no errors or gaps and having full applicability) beyond demonstrating a virtual compatibility/harmony, because one needs to solve all issues along the way in constructing invariants starting from moduli spaces to have a successful theory (for example, one issue solved in one way or by a trick might lead to difficulties in the upcoming constructions to be addressed and worked out). 