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I am looking for a reference for the definition 2.6 in https://ncatlab.org/nlab/show/simplicial+homotopy+group, which states "The simplicial homotopy groups of any simplicial set, not necessarily Kan, are those of any of its Kan fibrant replacements", as I can't find it anywhere. Thanks in advance.

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    $\begingroup$ I think the first deinition of that knd was given by Kan in his paper A combinatorial definition of homotopy groups. It is given using the $Ex^\infty$ functor in section 4 (which is curiously numbered as 5). It is pretty standard to see that any other fibrant replacement has the same homotopy groups. $\endgroup$
    – Andrea Gagna
    Commented Aug 9, 2018 at 12:41

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