Restriction categories II: Partial map classification

J. R B Cockett, Stephen Lack*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)61-102
Number of pages42
JournalTheoretical Computer Science
Issue number1-2
Publication statusPublished - 15 Feb 2003
Externally publishedYes


  • Kleisli category
  • Monad
  • Partial map classifier
  • Restriction category


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