---
res:
bibo_abstract:
- 'An object X of a category is said to have the projection property if the only
idempotent morphisms f : X x X --> X are the projections. Here a morphism f :
X x X --> X is called idempotent if f circle Delta = id for the diagonal map Delta
: X --> X x X. There are two motivations for studying the question whether X has
the projection property. Firstly, Arrow''s ''dictator theorem'' states that the
only maps of a product XA to X with certain properties are the projections (see
Arrow, 1963; Pouzet et al. 1996). Secondly, the projection property is closely
related to the fixed point property (see Corominas, 1990). In that paper the projection
property has been introduced for posets. It has been studied in a more general
setting by Davey et al. (1994) and Pouzet et al. (1996). For a detailed discussion
of the projection property, its background and connections with other properties
see also the paper by Pouzet (this volume). In this paper we prove that an irreducible
building of spherical type and of rank at least 2 has the projection property.
Actually, the theorem is more general. It holds not only for the case of a product
of two copies of X but for any finite number of copies of X and is thus similar
to Arrow''s theorem. For a precise statement of the hypotheses see below. By contrast,
every reducible building and every building of rank one does not have the projection
property. We also give a counterexample concerning the finiteness assumption of
the theorem. (C) 1998 Published by Elsevier Science B.V. All rights reserved.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Herbert
foaf_name: Abels, Herbert
foaf_surname: Abels
foaf_workInfoHomepage: http://www.librecat.org/personId=10478
bibo_doi: 10.1016/s0012-365x(98)00062-4
bibo_issue: 1-3
bibo_volume: 192
dct_date: 1998^xs_gYear
dct_identifier:
- UT:000076420800002
dct_isPartOf:
- http://id.crossref.org/issn/0012-365X
dct_language: eng
dct_publisher: Elsevier@
dct_title: A projection property for buildings@
...