Cosimplicial monoids and deformation theory of tensor categories
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00577958" target="_blank" >RIV/67985840:_____/23:00577958 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/23:10474461
Result on the web
<a href="https://doi.org/10.4171/jncg/512" target="_blank" >https://doi.org/10.4171/jncg/512</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/JNCG/512" target="_blank" >10.4171/JNCG/512</a>
Alternative languages
Result language
angličtina
Original language name
Cosimplicial monoids and deformation theory of tensor categories
Original language description
We introduce the notion of n-commutativity (0 ≤ n ≤ ∞) for cosimplicial monoids in a symmetric monoidal category V, where n = 0 corresponds to just cosimplicial monoids in V, while n=∞ corresponds to commutative cosimplicial monoids. When V has a monoidal model structure, we endow (under some mild technical conditions) the total object of an n-cosimplicial monoid with a natural and very explicit En+1-algebra structure. Our main applications are to the deformation theory of tensor categories and tensor functors.We show that the deformation complex of a tensor functor is a total complex of a 1-commutative cosimplicial monoid and, hence, has an E2-algebra structure similar to the E2-structure on Hochschild complex of an associative algebra provided by Deligne’s conjecture. We further demonstrate that the deformation complex of a tensor category is the total complex of a 2-commutative cosimplicial monoid and, therefore, is naturally an E3-algebra. We make these structures very explicit through a language of Delannoy paths and their noncommutative liftings. We investigate how these structures manifest themselves in concrete examples.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GX19-28628X" target="_blank" >GX19-28628X: Homotopy and Homology Methods and Tools Related to Mathematical Physics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Noncommutative Geometry
ISSN
1661-6952
e-ISSN
1661-6960
Volume of the periodical
17
Issue of the periodical within the volume
4
Country of publishing house
CH - SWITZERLAND
Number of pages
63
Pages from-to
1167-1229
UT code for WoS article
001108695100007
EID of the result in the Scopus database
2-s2.0-85175016218