Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cosmoi of internal categories


Author: Ross Street
Journal: Trans. Amer. Math. Soc. 258 (1980), 271-318
MSC: Primary 18D35; Secondary 18C10, 18F20
MathSciNet review: 558176
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 18D35, 18C10, 18F20

Retrieve articles in all journals with MSC: 18D35, 18C10, 18F20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0558176-3
PII: S 0002-9947(1980)0558176-3
Keywords: Internal full subcategory, locally presentable category, locally small, fibred category, site, sketched structures, Gabriel theory, internally complete, cartesian closed, multiple category
Article copyright: © Copyright 1980 American Mathematical Society