Notes on limits of accessible categories
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00599949" target="_blank" >RIV/67985840:_____/24:00599949 - isvavai.cz</a>
Result on the web
<a href="https://cahierstgdc.com/wp-content/uploads/2024/10/Positetski-LXV-4.pdf" target="_blank" >https://cahierstgdc.com/wp-content/uploads/2024/10/Positetski-LXV-4.pdf</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Notes on limits of accessible categories
Original language description
Let k be a regular cardinal, lambda < k be a smaller infinite cardinal, and K be a k-accessible category where colimits of lambda-indexed chains exist. We show that various category-theoretic constructions applied to K, such as the inserter and the equifier, produce k-accessible categories E again, and the most obvious expected description of the full subcategory of k-presentable objects in E in terms of k-presentable objects in K holds true. In particular, if C is a k-small category, then the category of functors C rightarrow K is k-accessible, and its k-presentable objects are precisely all the functors from C to the k-presentable objects of K. We proceed to discuss the preservation of k-accessibility by conical pseudolimits, lax and oplax limits, and weighted pseudolimits. The results of this paper go back to an unpublished 1977 preprint of Ulmer. Our motivation comes from the theory of flat modules and flat quasi-coherent sheaves.
Czech name
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Czech description
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Classification
Type
J<sub>ost</sub> - Miscellaneous article in a specialist periodical
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA23-05148S" target="_blank" >GA23-05148S: Homological and structural theory in geometric contexts</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Cahiers de Topologie et Géométrie Différentielle Catégoriques
ISSN
1245-530X
e-ISSN
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Volume of the periodical
65
Issue of the periodical within the volume
4
Country of publishing house
FR - FRANCE
Number of pages
48
Pages from-to
390-437
UT code for WoS article
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EID of the result in the Scopus database
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