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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cosmoi of internal categories
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by Ross Street PDF
Trans. Amer. Math. Soc. 258 (1980), 271-318 Request permission

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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Additional 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