On Finitary Functors and Their Presentations

  • Jiří Adámek
  • Stefan Milius
  • Lawrence S. Moss
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7399)

Abstract

Finitary endofunctors of locally presentable categories are proved to have equational presentations. Special attention is paid to the Hausdorff functor of non-empty compact subsets of a complete metric space.

Keywords

Finitary functors Hausdorff functor presentation of functors 

References

  1. 1.
    Abramsky, S., Jung, A.: Domain Theory. In: Handbook of Logic in Computer Science. Clarendon Press, Oxford (1994)Google Scholar
  2. 2.
    Adámek, J.: Free algebras and automata realizations in the language of categories. Comment. Math. Univ. Carolinae 15, 589–609 (1974)MathSciNetMATHGoogle Scholar
  3. 3.
    Adámek, J., Rosický, J.: Locally Presentable and Accessible Categories. Cambridge University Press (1993)Google Scholar
  4. 4.
    Adámek, J., Trnková, V.: Automata and Algebras in Categories. Kluwer Academic Publ., Dordrecht (1990)MATHGoogle Scholar
  5. 5.
    Adámek, J., Trnková, V.: Relatively terminal coalgebras. To appear in J. Pure Appl. AlgebraGoogle Scholar
  6. 6.
    Barr, M.: Terminal coalgebras in well-founded set theory. Theoret. Comput. Sci. 114, 299–315 (1993)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Borceux, F.: Handbook of Categorical Algebra, vol. 2. Cambridge University Press (1994)Google Scholar
  8. 8.
    van Breugel, F., Hermida, C., Makkai, M., Worrell, J.: Recursively defined metric spaces without contractionGoogle Scholar
  9. 9.
    Kelly, G.M., Power, J.: Adjunctions whose counits are coequalizers and presentations of finitary enriched monads. J. Pure Appl. Algebra 89, 163–179 (1993)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Lawvere, F.W.: Functional semantics of algebraic theories. Dissertation, Columbia University (1963)Google Scholar
  11. 11.
    Makkai, M., Paré, R.: Accessible Categories. Amer. Math. Soc., Providence, Rhode Island (1989)Google Scholar
  12. 12.
    Velebil, J., Kurz, A.: Equational presentations of functors and monads. Math. Structures Comput. Sci. 21, 363–381 (2011)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2012

Authors and Affiliations

  • Jiří Adámek
    • 1
  • Stefan Milius
    • 1
  • Lawrence S. Moss
    • 2
  1. 1.Institut für Theoretische InformatikTechnische Universität BraunschweigGermany
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

Personalised recommendations