Cosmoi of internal categories

Ross Street

doi:10.1090/S0002-9947-1980-0558176-3

Cosmoi of internal categories

Ross Street^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

Abstract

An internal full subcategory of a cartesian closed category ҩ is shown to give rise to a structure on the 2-category Cat(ҩ), of categories in ҩ which introduces the notion of size into the analysis of categories in ҩ 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.

Original language	English
Pages (from-to)	318
Number of pages	1
Journal	Transactions of the American Mathematical Society
Volume	258
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1980-0558176-3
Publication status	Published - 1980

Keywords

Cartesian closed
Fibred category
Gabriel theory
Internal full subcategory
Internally complete
Locally presentable category
Locally small
Multiple category
Site
Sketched structures

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10.1090/S0002-9947-1980-0558176-3

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KW - Cartesian closed

KW - Fibred category

KW - Gabriel theory

KW - Internal full subcategory

KW - Internally complete

KW - Locally presentable category

KW - Locally small

KW - Multiple category

KW - Site

KW - Sketched structures

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 2

ER -

Cosmoi of internal categories

Abstract

Keywords

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