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What are locally generated categories?

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Book cover Category Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1488))

Abstract

The answer to the question in the title, as given by Gabriel and Ulmer, is well enough known: precisely the locally presentable categories. We prove that the same result holds for mono-locally generated categories, a concept we introduce since we find it more “natural” than that of locally generated categories.

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References

  1. J. Adámek, H. Herrlich and G. Strecker,, Abstract and concrete categories, J. Wiley-Interscience Publ. New York, 1990.

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  2. J. Adámek and J. Rosický, Reflections in locally presentable categories, Arch. Math. (Brno) 25 (1989), 89–94.

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  3. J. Adámek, J. Rosický and V. Trnková, Are all limit-closed subcategories of locally presentable categories reflective?, Proc. Categ. Conf. Louvain-La-Neuve (1987); Lecture Notes in Math. 1348 (1988), 1–18, Springer-Verlag, Berlin.

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  4. P. Gabriel and F. Ulmer, Lokal präsentierbare Kategorien, Lect. Notes in Math. 221 (1971), Springer-Verlag, Berlin.

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  5. M. Makkai and R. Paré, Accessible categories: The foundations of categorical model theory, Contemporary Mathematics 104 (1989), Amer. Math. Society, Providence.

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  6. J. Rosický, V. Trnková and J. Adámek, Unexpected properties of locally presentable categories, Alg. Univ. 27 (1990), 153–170.

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Author information

Authors and Affiliations

  1. Technical University, Suchbátarova 2, 166 27, Prague, Czechoslovakia

    Jiří Adámek & Jiří Rosický

  2. Masaryk University, Janáčkovo Nám. 2A, 662 95, Brno, Czechoslovakia

    Jiří Adámek & Jiří Rosický

Authors
  1. Jiří Adámek
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  2. Jiří Rosický
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Editor information

Aurelio Carboni Maria Cristina Pedicchio Guiseppe Rosolini

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© 1991 Springer-Verlag

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Adámek, J., Rosický, J. (1991). What are locally generated categories?. In: Carboni, A., Pedicchio, M.C., Rosolini, G. (eds) Category Theory. Lecture Notes in Mathematics, vol 1488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084209

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  • DOI: https://doi.org/10.1007/BFb0084209

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54706-8

  • Online ISBN: 978-3-540-46435-8

  • eBook Packages: Springer Book Archive

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