1
$\begingroup$

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 $G={\mathbb{Z}}/2$.

  • 1
    "Every simplicial set is the colimit of its finite simplicial subsets. " Really? I doubt that this is true. Or what notion of "finite" are you working with here?2012-10-25
  • 0
    The obvious way of making the statement true is to replace "finite" by "finitely presented" (in the sense of Gabriel and Ulmer). But I think this turns out to be the same thing as a simplicial set with finitely many non-degenerate simplices.2012-10-25

1 Answers 1