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I am looking for a reader-friendly proof of the following theorem:

let $A$ be a special $\Gamma$-space then $\pi_0(A(S^0))$ is a commutative monoid (I have proved up to this), if further it is an abelian group then the adjoint map $t: A(S^0) \to \Omega{BA(S^0)}$ for the structure map $s: \Sigma(A(S^0)) \to BA(S^0)$ is a weak homotopy equivalence

Dan Freed in his notes theorem 19.41 points to Segal's paper as reference but I cannot find a proof there (did I miss it?).

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It is proposition 1.4 in Segal's Categories and cohomology theories (a paper I love and I strongly encourage everyone interested in homotopy theory to read).

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  • $\begingroup$ Yes! Have heard of that paper many times and now it is time for me to read it! Many thanks for pointing that out, Denis! $\endgroup$
    – PhysicsMath
    Commented Aug 15, 2016 at 20:48

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