Re: Undirected graphs citation

1 Mar 2006

      Vaughan Pratt asked about:
...
undirected graphs ...  as presheaves on the full subcategory 1 and
2 of Set?
It is the 2-truncation of "symmetric simplicial sets" as presheaves
on finite cardinals, cf (*).

Curiously, symmetric simplicial sets have been rarely considered.
Even if simplicial complexes (well-known!) are a symmetric notion and
have a natural embedding in symmetric simplicial sets.  While
simplicial sets are a directed notion, used as an undirected one in
classical Algebraic Topology.

(*) M. Grandis, Finite sets and symmetric simplicial sets, Theory
Appl. Categ. 8 (2001), No. 8, 244-252.

Marco Grandis