Operadic categories as a natural environment for Koszul duality

Result code in 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>

Alternative codes found

RIV/00216208:11320/23:10474463

Result on the web

<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>

Result language

angličtina

Original language name

Operadic categories as a natural environment for Koszul duality

Original language description

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.

Czech name

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Czech description

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Type

J_SC - Article in a specialist periodical, which is included in the SCOPUS database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Name of the periodical

Compositionality

ISSN

2631-4444

e-ISSN

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Volume of the periodical

5

Issue of the periodical within the volume

3

Country of publishing house

GB - UNITED KINGDOM

Number of pages

46

Pages from-to

1-46

UT code for WoS article

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EID of the result in the Scopus database

2-s2.0-85163795512