Homotopy units in $A$-infinity algebras
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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.References
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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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 2145-2184
- MSC (2010): Primary 18D50, 18G55
- DOI: https://doi.org/10.1090/tran/6545
- MathSciNet review: 3449236