Quasi-tame substitudes and the Grothendieck construction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00638443" target="_blank" >RIV/67985840:_____/25:00638443 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.tac.mta.ca/tac/volumes/44/24/44-24.pdf" target="_blank" >http://www.tac.mta.ca/tac/volumes/44/24/44-24.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Quasi-tame substitudes and the Grothendieck construction

Popis výsledku v původním jazyce

This paper continues the study of the homotopy theory of algebras over polynomial monads initiated by the first author and Clemens Berger. We introduce the notion of a quasi-tame polynomial monad (generalizing tame ones) and produce transferred model structures (left proper in many settings) on algebras over such a monad. Our motivating application is to produce model structures on Grothendieck categories, which are used in [BDW23] to give a unified approach to the study of operads, their algebras, and their modules. We prove a general result regarding when a Grothendieck construction can be realized as a category of algebras over a polynomial monad, examples illustrating that quasi-tameness is necessary as well as sufficient for admissibility, and an extension of classifier methods to a non-polynomial situation, namely the case of commutative monoids.

Název v anglickém jazyce

Quasi-tame substitudes and the Grothendieck construction

Popis výsledku anglicky

This paper continues the study of the homotopy theory of algebras over polynomial monads initiated by the first author and Clemens Berger. We introduce the notion of a quasi-tame polynomial monad (generalizing tame ones) and produce transferred model structures (left proper in many settings) on algebras over such a monad. Our motivating application is to produce model structures on Grothendieck categories, which are used in [BDW23] to give a unified approach to the study of operads, their algebras, and their modules. We prove a general result regarding when a Grothendieck construction can be realized as a category of algebras over a polynomial monad, examples illustrating that quasi-tameness is necessary as well as sufficient for admissibility, and an extension of classifier methods to a non-polynomial situation, namely the case of commutative monoids.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Theory and Applications of Categories

ISSN

1201-561X

e-ISSN

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Svazek periodika

44

Číslo periodika v rámci svazku

24

Stát vydavatele periodika

CA - Kanada

Počet stran výsledku

56

Strana od-do

676-730

Kód UT WoS článku

001546435800001

EID výsledku v databázi Scopus

2-s2.0-105013673758