Cosimplicial monoids and deformation theory of tensor categories

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216208:11320/23:10474461

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Cosimplicial monoids and deformation theory of tensor categories

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Cosimplicial monoids and deformation theory of tensor categories

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX19-28628X" target="_blank" >GX19-28628X: Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Noncommutative Geometry

ISSN

1661-6952

e-ISSN

1661-6960

Svazek periodika

17

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

63

Strana od-do

1167-1229

Kód UT WoS článku

001108695100007

EID výsledku v databázi Scopus

2-s2.0-85175016218