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A projection property

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Abstract

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 ε 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.

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Authors and Affiliations

  1. Institut de Mathématique-Informatique, Université Claude Bernard LYON 1, 43 Bd 11 Novembre 1918, F-69622, Villeurbanne Cédex, France

    M. Pouzet

  2. Départment de Mathématiques et Statistique, Université de Montréal, H3C 3J7, Québec, Canada

    I. G. Rosenberg

  3. Department of Mathematics and Statistics, University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    M. G. Stone

Authors
  1. M. Pouzet
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  2. I. G. Rosenberg
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  3. M. G. Stone
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Additional information

Author supported by the French group PRC Math-Info, and NSERC of Canada.

Author supported by NSERC Grant OGP 5407 and FCAR Québec grant Eq 0537.

Author supported by NSERC Grant 69-3039.

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Pouzet, M., Rosenberg, I.G. & Stone, M.G. A projection property. Algebra Universalis 36, 159–184 (1996). https://doi.org/10.1007/BF01234102

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