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On the notion of bimodel for functorial semantics

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We discuss the notion of bimodel in order to obtain a classification of the equivalences between categories of models in the sense of functorial semantics.

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References

  1. Barr M. and Wells C.:Toposes, Triples and Theories, Grundleheren der Mathematischen Wissenschaften 278, Springer-Verlag, Berlin-Heidelberg-New York (1984).

    Google Scholar 

  2. Bass H.:Algebraic K-Theory W. A. Benjamin Inc., New York (1968).

    Google Scholar 

  3. Benabou J.: Les Distributeurs,Rap. Sém. Math. Pures 33, Univ. Louvain (1973).

  4. Borceux F.:A Handbook of Categorical Algebra, Cambridge University Press (to appear).

  5. Dukarm J.: Morita Equivalence of Algebraic Theories,Colloquium Mathematicum 55 (1988), 11–17.

    Google Scholar 

  6. Elkins B. and Zilber J.: Categories of Actions and Morita Equivalences,Rocky Mountain J. Math. 6 (1976), 199–225.

    Google Scholar 

  7. Freyd P.: Algebra Valued Functors in General and Tensor Products in Particular,Colloquium Mathematicum 14 (1966), 89–106.

    Google Scholar 

  8. Gabriel P. and Ulmer F.:Lokal Präsentierbare Kategorien, Springer Lecture Notes 221 (1971).

  9. Lawvere F.W.: Functorial Semantics of Algebraic Theories, Ph. D. Thesis Columbia University (1963).

  10. Lawvere F.W.: Metric Spaces, Generalized Logic and Closed Categories,Rend. Sem. Mat. e Fisico di Milano 43 (1973), 135–166.

    Google Scholar 

  11. Linton F.: Some Aspects of Equational Categories,Proceedings of the Conference on Categorical Algebra (La Jolla, 1965), Springer-Verlag, Berlin-Heidelberg-New York (1966).

    Google Scholar 

  12. Mac Lane S.:Categories for the Working Mathematician Graduate Texts in Mathematics 5, Springer-Verlag, Berlin-Heidelberg-New York (1971).

    Google Scholar 

  13. Makkai M. and Paré R.: Accessible Categories: the Foundations of Categorical Model Theory,Contemporary Mathematics 104, Amer Math Society, Providence (1989).

    Google Scholar 

  14. Pultr A.:The Right Adjoints into the Categories of Relational Systems, Reports Midwest Category Seminar IV, Springer Lecture Notes 137 (1970), pp. 100–113.

  15. Schubert H.:Categories Springer-Verlag, Berlin-Heidelberg-New York (1972).

    Google Scholar 

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Research supported by NATO grant 900959 and FNRS grant 1.5.181.90F

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Borceux, F., Vitale, E.M. On the notion of bimodel for functorial semantics. Appl Categor Struct 2, 283–295 (1994). https://doi.org/10.1007/BF00878101

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