simplicial skeleton

Last updated January 27, 2022

Relation to homotopy

1. For each $n\in\mathbb{N}$, the unit of the adjunction $$X\to\textbf{cosk}_n(X)$$ induces an isomorphism on all simplicial homotopy groups in degree $<n$.
   1. If $X$ is an $n$-coskeletal Kan complex, all its simplicial homotopy groups above degree $(n-1)$ are trivial.