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This article is the second part of the article we promised to write at theend of Section 1 of [FOOO15] (arXiv:1209.4410). (Part I appeared in [Part I](arXiv:1503.07631).) We discuss the foundation of the virtual fundamental chainand cycle technique, especially its version that appeared in [FOn] and also inSection A1, Section 7.5 [FOOO4], Section 12 [FOOO7], [Fu2]. This article isindependent of our earlier writing [FOOO15]. We also do not assume that thereaders have any knowledge on the pseudo-holomorphic curve. In this secondpart, we consider a system of spaces with Kuranishi structures (abbreviated asa K-system) and its simultaneous perturbations.

Kuranishi structure, Pseudo-holomorphic curve, and virtual fundamental chain: Part 2