Operadic categories as a natural environment for Koszul duality

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00572905" target="_blank" >RIV/67985840:_____/23:00572905 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/23:10474463

Výsledek na webu

<a href="https://doi.org/10.32408/compositionality-5-3" target="_blank" >https://doi.org/10.32408/compositionality-5-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.32408/compositionality-5-3" target="_blank" >10.32408/compositionality-5-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Operadic categories as a natural environment for Koszul duality

Popis výsledku v původním jazyce

This is the first paper of a series which aims to set up the cornerstones of Koszul duality for operads over operadic categories. To this end we single out additional properties of operadic categories under which the theory of quadratic operads and their Koszulity can be developed, parallel to the traditional one by Ginzburg–Kapranov. We then investigate how these extra properties interact with discrete operadic (op)fibrations, which we use as a powerful tool to construct new operadic categories from old ones. We pay particular attention to the operadic category of graphs, giving a full description of this category (and its variants) as an operadic category, and proving that it satisfies all the additional properties.nOur present work provides an answer to a question formulated in Loday's last talk, in 2012: 'What encodes types of operads?'. In the second and third papers of our series we continue Loday's program by answering his second question: 'How to construct Koszul duals to these objects?', and proving Koszulity of some of the most relevant operads.

Název v anglickém jazyce

Operadic categories as a natural environment for Koszul duality

Popis výsledku anglicky

This is the first paper of a series which aims to set up the cornerstones of Koszul duality for operads over operadic categories. To this end we single out additional properties of operadic categories under which the theory of quadratic operads and their Koszulity can be developed, parallel to the traditional one by Ginzburg–Kapranov. We then investigate how these extra properties interact with discrete operadic (op)fibrations, which we use as a powerful tool to construct new operadic categories from old ones. We pay particular attention to the operadic category of graphs, giving a full description of this category (and its variants) as an operadic category, and proving that it satisfies all the additional properties.nOur present work provides an answer to a question formulated in Loday's last talk, in 2012: 'What encodes types of operads?'. In the second and third papers of our series we continue Loday's program by answering his second question: 'How to construct Koszul duals to these objects?', and proving Koszulity of some of the most relevant operads.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

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

Compositionality

ISSN

2631-4444

e-ISSN

—

Svazek periodika

5

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

46

Strana od-do

1-46

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85163795512