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On essentially algebraic theorries and their generalizations

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Abstract.

A new proof of the fact that locally presentable categories precisely correspond to essentially algebraic theories is presented. An analogous result for locally generated categories is obtained. And in the same vein Diers’ locally multipresentable categories are characterized via essentially multialgebraic theories, and they are generalized to locally multigenerated categories.

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Authors and Affiliations

  1. Institut für Theoretische Informatik, Technical University Braunschweig, Postfach 3329, D-38023 Braunschweig, Germany, e-mail: adamek@iti.cs.tu-bs.de, , , , , , DE

    J. Adámek

  2. Mathematics Unit, The American University in Cairo, Box 2511, Cairo 11511, Egypt, e-mail: mhebert@aucegypt.edu, , , , , , EG

    M. Hébert

  3. Department of Algebra and Geometry, Masaryk University, Janáčkovo nám. 2a, CZ-662 95 Brno, Czech Republic, e-mail: rosicky@math.muni.cz, , , , , , CZ

    J. Rosický

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  1. J. Adámek
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  2. M. Hébert
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  3. J. Rosický
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Received July 21, 1998; accepted in final form February 24, 1999.

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Adámek, J., Hébert, M. & Rosický, J. On essentially algebraic theorries and their generalizations. Algebra univers. 41, 213–227 (1999). https://doi.org/10.1007/s000120050111

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  • DOI: https://doi.org/10.1007/s000120050111

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