Iterated algebraic injectivity and the faithfulness conjecture

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114577" target="_blank" >RIV/00216224:14310/20:00114577 - isvavai.cz</a>

Výsledek na webu

<a href="https://journals.mq.edu.au/index.php/higher_structures/article/view/120/81" target="_blank" >https://journals.mq.edu.au/index.php/higher_structures/article/view/120/81</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Iterated algebraic injectivity and the faithfulness conjecture

Popis výsledku v původním jazyce

Algebraic injectivity was introduced to capture homotopical structures like algebraic Kan complexes. But at a much simpler level, it allows one to describe sets with operations subject to no equations. If one wishes to add equations (or operations of greater complexity) then it is natural to consider iterated algebraic injectives, which we introduce and study in the present paper. Our main application concerns Grothendieck's weak omega-groupoids, introduced in Pursuing Stacks, and the closely related definition of weak omega-category due to Maltsiniotis. Using omega iterations we describe these as iterated algebraic injectives and, via this correspondence, prove the faithfulness conjecture of Maltsiniotis. Through work of Ara, this implies a tight correspondence between the weak omega-categories of Maltsiniotis and those of Batanin/Leinster.

Název v anglickém jazyce

Iterated algebraic injectivity and the faithfulness conjecture

Popis výsledku anglicky

Algebraic injectivity was introduced to capture homotopical structures like algebraic Kan complexes. But at a much simpler level, it allows one to describe sets with operations subject to no equations. If one wishes to add equations (or operations of greater complexity) then it is natural to consider iterated algebraic injectives, which we introduce and study in the present paper. Our main application concerns Grothendieck's weak omega-groupoids, introduced in Pursuing Stacks, and the closely related definition of weak omega-category due to Maltsiniotis. Using omega iterations we describe these as iterated algebraic injectives and, via this correspondence, prove the faithfulness conjecture of Maltsiniotis. Through work of Ara, this implies a tight correspondence between the weak omega-categories of Maltsiniotis and those of Batanin/Leinster.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-00902S" target="_blank" >GA19-00902S: Injektivita a monády v algebře a topologii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Higher Structures

ISSN

2209-0606

e-ISSN

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Svazek periodika

4

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

AU - Austrálie

Počet stran výsledku

28

Strana od-do

183-210

Kód UT WoS článku

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EID výsledku v databázi Scopus

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