Iterated algebraic injectivity and the faithfulness conjecture

Result code in 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>
Result on the web
<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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Result language
angličtina
Original language name
Iterated algebraic injectivity and the faithfulness conjecture
Original language description
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.
Czech name
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Czech description
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Project
<a href="/en/project/GA19-00902S" target="_blank" >GA19-00902S: Injectivity and Monads in Algebra and Topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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