Every simplicial set is the colimit of its finite simplicial subsets. Suppose $G$ be a finite discrete set.
Is every simplicial $G$-set a colimit of its finite simplicial $G$-subsets? I'm particularly interested in the case where $G={\mathbb{Z}}/2$.
2026-03-29 07:29:14.1774769354
Decomposition of simplicial G-sets as a colimits of its simplicial G-subsets
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I assume you meant $G$ should be a finite discrete group? Also, I think the answer is yes. Every simplex of a $G$-sset is contained in a finite sub-sset, and then you you can take the closure under the $G$-action (which will still be finite, since $G$ is). This closure will be a sub-sset because the face and degeneracy maps are $G$-equivariant.