HSP type theorems in the category of posets

  • Michael Barr
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 598)

Abstract

This paper introduces the notion of a theory based on posets and HSP or Birkhoff subcategories thereof. It turns out that the nature of these subcategories depends on what is meant by subobject. The correspondence between subcategories does not hold as it does in sets, primarily because the axiom of choice (in the form that epimorphisms split) totally fails in posets. Although equations, suitably generalized to include inequalities, determine HSP subcategories, the converse fails and it may be necessary to iterate the process of forming the subcategories by means of equations and inequalities.

Keywords

Factorization System Natural Transformation Full Subcategory Horn Clause Left Adjoint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Michael Barr

There are no affiliations available

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