Applied Categorical Structures

, Volume 1, Issue 4, pp 423–440 | Cite as

The algebraic theory of order

  • Hans-E. Porst


Partially ordered sets are described in terms of partial operations with equationally defined domains and equations, thus the categoryPOS of posets is represented as a one-sorted essentially algebraic category in the sense of Freyd [7] which, in this case even can be fully embedded into a non-trivial variety. This is achieved by using the relation of a poset rather than its underlying set as the carrier set of the algebraic structure. Essentially equational descriptions of somePOS-based algebraic structures are given, and an equational characterization of Galois connections is obtained.

Mathematics Subject Classifications (1991)

Primary 06A06 06A15 06F99 Secondary 08A55 18B35 

Key words

Essentially equational theory essentially algebraic category order and preorder ordered algebras 


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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Hans-E. Porst
    • 1
  1. 1.Fachbereich Mathematik und InformatikUniversität BremenBremenGermany

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