Restriction categories II: partial map classification

  • Authors:

  • J. R. B. Cockett;Stephen Lack

  • Affiliations:

  • Department of Computer Science, University of Calgary, Calgary, Alberta, Canada T2N 1N4;Department of Mathematics and Statistics, University of Sydney, F07-Carslaw, Sydney, NSW 2006, Australia

  • Venue:
  • Theoretical Computer Science - Category theory and computer science
  • Year:
  • 2003

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Abstract

An algebraic characterization of monads which are abstract partial map classifiers is provided, without the assumption that the categories of total maps possess products. By an abstract partial map classifier we mean a monad whose Kleisli category is a full subcategory of a partial map category wherein the induced comonad classifies partial maps in the usual sense. A construction of the corresponding actual partial map classifier from an abstract one is described, and conditions for an abstract partial map classifier to be a real one are provided. The paper uses the notion of a restriction category developed in earlier work, and the characterization of these as full subcategories of partial map categories.