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Algebra ∩ Coalgebra = Presheaves

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Algebra and Coalgebra in Computer Science (CALCO 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3629))

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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.

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References

  1. Adámek, J., Porst, H.-E.: On varieties and covarieties in a category. Math. Structures Comput. Sci. 13, 201–232 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Loeckx, J., Ehrich, H.-D., Wolf, M.: Specification of abstract data types. Wiley and Teubner, Chichester (1996)

    MATH  Google Scholar 

  3. 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. MacLane, S.: Categories for the working mathematician. Springer, Heidelberg (1971)

    Google Scholar 

  5. Porst, H.-E.: What is concrete equivalence? Appl. Categorical Structures 2, 57–70 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  6. 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)

    Chapter  Google Scholar 

  7. Reiterman, J.: One more cagorical model of universal algebra. Math. Z. 161, 137–146 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  8. Rutten, J.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249, 3–80 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Trnková, V.: Some properties of set functors. Comment Math. Univ. Carolinae 10, 323–352 (1969)

    MATH  MathSciNet  Google Scholar 

  10. Trnková, V.: On descriptive classification of set-functors I. Comment. Math. Univ. Carolinae 12, 143–174 (1971)

    MATH  MathSciNet  Google Scholar 

  11. Worrell, J.: A note on coalgebras and presheaves. Electr. Notes Theor. Comput. Sci. 65(1) (2002)

    Google Scholar 

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Adámek, J. (2005). Algebra ∩ Coalgebra = Presheaves. In: Fiadeiro, J.L., Harman, N., Roggenbach, M., Rutten, J. (eds) Algebra and Coalgebra in Computer Science. CALCO 2005. Lecture Notes in Computer Science, vol 3629. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548133_5

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  • DOI: https://doi.org/10.1007/11548133_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28620-2

  • Online ISBN: 978-3-540-31876-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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