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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Cosmoi of internal categories
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by Ross Street
Trans. Amer. Math. Soc. 258 (1980), 271-318
DOI: https://doi.org/10.1090/S0002-9947-1980-0558176-3

Abstract:

An internal full subcategory of a cartesian closed category $\mathcal {A}$, is shown to give rise to a structure on the 2-category $Cat(\mathcal {A})$ of categories in $\mathcal {A}$ which introduces the notion of size into the analysis of categories in $\mathcal {A}$ and allows proofs by transcendental arguments. The relationship to the currently popular study of locally internal categories is examined. Internal full subcategories of locally presentable categories (in the sense of Gabriel-Ulmer) are studied in detail. An algorithm is developed for their construction and this is applied to the categories of double categories, triple categories, and so on.
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Bibliographic Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 258 (1980), 271-318
  • MSC: Primary 18D35; Secondary 18C10, 18F20
  • DOI: https://doi.org/10.1090/S0002-9947-1980-0558176-3
  • MathSciNet review: 558176