In geometry, a flag is a chain of incidence relations, as for example between distinct linear subspaces
of a fixed vector space , or between isotropic subspaces, etc.
Flags of posets
Generally speaking, if is a poset, a flag is a chain
and the set of elements can be thought of as an -simplex of a simplicial complex whose vertices are the poset elements. Hence we have a functor
In the other direction, there is an underlying functor
which sends a simplicial complex to (regarded as a poset ordered by inclusion). The composite
is called the subdivision functor, or, more exactly, the barycentric subdivision functor.
Revised on September 4, 2013 14:41:22
by Urs Schreiber