Suppose we have a fibrant simplicial set $X$ with base point $v$. Suppose we have simplex $z\in X_{n+1}$ such that $d_0(z) = x, d_1(z) = ... = d_n(z) = v, d_{n+1}(z) = y$, where $x$ and $y$ are some simplices in $X_n$ with all faces equal to $v$. Is it true then that $[x] = [y]^{(-1)^n}\in \pi_n(X,v)$? Here $[x]$ is a homotopy class represented by $x$, as usual.
Пацаны, понимаю что вопрос дико уныл, но в натуре надо разобраться,а то на душе неспокойно