]{} is an augmented simplicial object ${\ensuremath{\mathbb{T}}}$ equipped with a simplicial morphism ${\ensuremath{\mathbb{t}}}\colon {{\ensuremath{\mathbb{T}}}\to {\ensuremath{\mathbb{K}}}(Z,A,n)}$ such that  0.  ${\ensuremath{\mathbb{t}}}$ is a fibration which is exact from degree $n$ on;  0.  ${\ensuremath{\mathbb{T}}}\cong {\ensuremath{\mathsf{Cosk}}}_{n-0}{\ensuremath{\mathbb{T}}}$