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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Homotopy units in $ A$-infinity algebras


Author: Fernando Muro
Journal: Trans. Amer. Math. Soc. 368 (2016), 2145-2184
MSC (2010): Primary 18D50, 18G55
DOI: https://doi.org/10.1090/tran/6545
Published electronically: May 8, 2015
MathSciNet review: 3449236
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Abstract: We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative algebra structures on a given object is up to homotopy a subset of connected components of the space of non-unital associative algebra structures.


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Additional Information

Fernando Muro
Affiliation: Facultad de Matemáticas, Departamento de Álgebra, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain
Email: fmuro@us.es

DOI: https://doi.org/10.1090/tran/6545
Keywords: Operad, $A$-infinity algebra, unit, model category, mapping space.
Received by editor(s): August 21, 2013
Received by editor(s) in revised form: February 17, 2014, April 22, 2014, and July 29, 2014
Published electronically: May 8, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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