Detailed Information on Publication Record
2024
Accessible categories with a class of limits
LACK, Stephen and Giacomo TENDASBasic information
Original name
Accessible categories with a class of limits
Authors
LACK, Stephen and Giacomo TENDAS (380 Italy, belonging to the institution)
Edition
Journal of Pure and Applied Algebra, Elsevier B.V. 2024, 0022-4049
Other information
Language
English
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
Netherlands
Confidentiality degree
není předmětem státního či obchodního tajemství
References:
Impact factor
Impact factor: 0.800 in 2022
Organization unit
Faculty of Science
UT WoS
001034156000001
Keywords in English
Enriched categories; Accessible and locally presentable categories; Sketches and generalizations
Tags
Tags
International impact, Reviewed
Změněno: 3/1/2024 11:53, Mgr. Marie Šípková, DiS.
Abstract
V originále
In this paper we characterize those accessible V-categories that have limits of a specified class. We do this by introducing the notion of companion C for a class of weights Ψ, as a collection of special types of colimit diagrams that are compatible with Ψ. We then characterize the accessible V-categories with Ψ-limits as those accessibly embedded and C-virtually reflective in a presheaf V-category, and as the V-categories of C-models of sketches. This allows us to recover the standard theorems for locally presentable, locally multipresentable, and locally polypresentable categories as instances of the same general framework. In addition, our theorem covers the case of any weakly sound class Ψ, and provides a new perspective on the case of weakly locally presentable categories.
Links
| GA22-02964S, research and development project |
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