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  3. Locally Presentable and Accessible Categories
  • Cited by 427
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    • Publisher:
      Cambridge University Press
      Publication date:
      15 December 2009
      10 March 1994
      ISBN:
      9780511600579
      9780521422611
      DOI:
      https://doi.org/10.1017/CBO9780511600579
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.489kg, 332 Pages
      • Subjects:
      Mathematics (general), Mathematics, Logic, Categories and Sets, Algebra
      Series:
      London Mathematical Society Lecture Note Series (189)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Logic, Categories and Sets, Algebra
    Series:
    London Mathematical Society Lecture Note Series (189)
    Information

    Book description

    The concepts of a locally presentable category and an accessible category have turned out to be useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students. Firstly the properties of l-presentable objects, locally l-presentable categories, and l-accessible categories are discussed in detail, and the equivalence of accessible and sketchable categories is proved. The authors go on to study categories of algebras and prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapters they treat some topics in model theory and some set theoretical aspects. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.

    Reviews

    "...the authors have taken the indicated material, organized it effectively, written a very lucid, readable development of it in 280 pages, and added helpful historical remarks to each chapter and a brief appendix on large cardinals. There are some novel results...most notably a significant improvement of the Gabriel-Ulmer theorem on "local generation" of locally presentable categories." J.R. Isbell, Mathematical Reviews

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