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Simplicial set represented by an (unordered) set Simplicial space and its simplicial replacement?Hodge star and harmonic simplicial differential formsCech nerve as homotopy colimit?Removing a simplicial subset from a simplicial setVector fields on a simplicial manifold.Is there a class of simplicial sets whose weak homotopy type is preserved by symmetrization?What suffices to check completeness in an n-fold Segal space?explicit description of the cosimplicial simplicial set $Q^bullet$Why are simplicial objects monadic over split (contractible) simplicial objects?Is totalization (of a cosimplicial category) a part of some adjunction? 1 $begingroup$ Let $X$ be a (finite if you want) set and form the simplicial set $F^bullet(X)$ with $$ F^n(X) = mathrmHom_mathrmset ([n], X) $$ where the right hand side denotes arbitrary maps of sets (of course it wouldn't make sense to say order preserving as $X$ doesn't come with an order). I'm wondering about a description