Homotopy theory of algebras of substitudes and their localisation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00556688" target="_blank" >RIV/67985840:_____/22:00556688 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/tran/8600" target="_blank" >https://doi.org/10.1090/tran/8600</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/tran/8600" target="_blank" >10.1090/tran/8600</a>
Alternative languages
Result language
angličtina
Original language name
Homotopy theory of algebras of substitudes and their localisation
Original language description
We study the category of algebras of substitudes (also known to be equivalent to the regular patterns of Getzler and operads coloured by a category) equipped with a (semi)model structure lifted from the model structure on the underlying presheaves. We are especially interested in the case when the model structure on presheaves is a Cisinski style localisation with respect to a proper Grothendieck fundamental localiser. For example, for the minimal fundamental localiser, the local objects in such a localisation are locally constant presheaves, and local algebras of substitudes are exactly algebras whose underlying presheaves are locally constant.nWe investigate when this localisation has nice properties. We single out a class of such substitudes which we call left localisable and show that the substitudes for -operads, symmetric, and braided operads are in this class. As an application we develop a homotopy theory of higher braided operads and prove a stabilisation theorem for their -localisations. This theorem implies, in particular, a generalisation of the Baez-Dolan stabilisation hypothesis for higher categories.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
American Mathematical Society. Transactions
ISSN
0002-9947
e-ISSN
1088-6850
Volume of the periodical
375
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
72
Pages from-to
3569-3640
UT code for WoS article
000807482000016
EID of the result in the Scopus database
2-s2.0-85127956772