I think an answer of this question is well-explained in (3.7) of S. Kumar, Infinite Grassmannians and moduli spaces of G-bundles(New directions).

I think I understood what I missed. I appreciate for all comments :)

I forgot to write something. In this case, $E_i$'s are complex vector bundles. Is it possible to induce complex structure to the orthogonal complement of $E_i$? It looks little strange for me because then, if the base space is paracompact, then every short exact sequence splits!. In general, it never happens in algebraic geometry. What is a difference when there is a metric?

On the other hand, why $\mathrm{map}(S^1,X)$ is isomorphic to $X$?

Sorry I'm little confusing. What is a definition of $\mathrm{map}(S^n,X)$? I think $X$ lives in the category of functors from $\mathrm{Ho}(sComm)^{op}$ to $\mathrm{SSet}$. Is it make sence to consider a map space from $S^n$ to $X$?

Thank you. I think you know something and have intuition. Since I'm a just beginner of derived algebraic geometry, I cannot understand that n-geometric is equivalent to that higher diagonal $X \to map(S^n, X)$ is affine. May I ask you the reason why? Is there a theorem saying this in HAG2?

Thank you for Jason and Honglu and I'm sorry for my late reply. I also found a good reference for degree zero Gromov-Witten invariant written by R. Pandharipande : arxiv.org/abs/math/0302077