Advertisement

Abstract

The intersection of algebra and coalgebra, i.e., the collection of all categories that are varieties as well as covarieties, is proved to consist of precisely the presheaf categories.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AP]
    Adámek, J., Porst, H.-E.: On varieties and covarieties in a category. Math. Structures Comput. Sci. 13, 201–232 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  2. [LEW]
    Loeckx, J., Ehrich, H.-D., Wolf, M.: Specification of abstract data types. Wiley and Teubner, Chichester (1996)zbMATHGoogle Scholar
  3. [LP]
    Linton, F.E.J., Paré, R.C.: Injectives in topoi I: Representing coalgebras as algebras. Lect. Notes Mathem., vol. 719, pp. 196–206. Springer, Heidelberg (1970)Google Scholar
  4. [M]
    MacLane, S.: Categories for the working mathematician. Springer, Heidelberg (1971)Google Scholar
  5. [P]
    Porst, H.-E.: What is concrete equivalence? Appl. Categorical Structures 2, 57–70 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  6. [PD]
    Porst, H.-E., Dzieron, C.: On coalgebras which are algebras. In: Gähler, Preuss (eds.) Categorical Structures and Applications, pp. 227–234. World Scientific Publ., Singapore (2004)CrossRefGoogle Scholar
  7. [Re]
    Reiterman, J.: One more cagorical model of universal algebra. Math. Z. 161, 137–146 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  8. [Ru]
    Rutten, J.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249, 3–80 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  9. [T1]
    Trnková, V.: Some properties of set functors. Comment Math. Univ. Carolinae 10, 323–352 (1969)zbMATHMathSciNetGoogle Scholar
  10. [T2]
    Trnková, V.: On descriptive classification of set-functors I. Comment. Math. Univ. Carolinae 12, 143–174 (1971)zbMATHMathSciNetGoogle Scholar
  11. [W]
    Worrell, J.: A note on coalgebras and presheaves. Electr. Notes Theor. Comput. Sci. 65(1) (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • J. Adámek
    • 1
  1. 1.Technical University of Braunschweig 

Personalised recommendations