Skip to main content

What are locally generated categories?

Part I

Part of the Lecture Notes in Mathematics book series (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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  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.

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    CrossRef  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54706-8

  • Online ISBN: 978-3-540-46435-8

  • eBook Packages: Springer Book Archive