  In this paper we study quotients of posets by group actions. In order to
define the quotient correctly we enlarge the considered class of categories
from posets to loopfree categories: categories without nontrivial automorphisms
and inverses. We view group actions as certain functors and define the
quotients as colimits of these functors. The advantage of this definition over
studying the quotient poset (which in our language is the colimit in the poset
category) is that the realization of the quotient loopfree category is more
often homeomorphic to the quotient of the realization of the original poset. We
give conditions under which the quotient commutes with the nerve functor, as
well as conditions which guarantee that the quotient is again a poset.
