A projection property

Autor: M. G. Stone, Maurice Pouzet, Ivo G. Rosenberg
Rok vydání: 1996
Předmět:
Zdroj: Algebra Universalis. 36:159-184
ISSN: 1420-8911
0002-5240
Popis: E. Corominas introduced recently this notion for posets:P is projective if every mapf fromP 2 toP which is order preserving and idempotent (i.e.f(x, x)=x for allx e P) is a projection. We consider extensions of this notion to other structures, as well as to maps withn variables. We prove thatn-projectivity forn≥2 is equivalent to 2-projectivity, with a single exception: the structure has the same morphisms as the collection of congruences associated with a vector space over ℤ/2, of dimension at least two. Focusing on relational structures, Arrow's Theorem is introduced as an example. We consider particular types of relational structures: posets, graphs and metric spaces, and discuss for these the specific examples of crowns, cycles and circles.
Databáze: OpenAIRE
Externí odkaz: