Title 



On a higher structure on operadic deformation complexes
 
Author 


  
Abstract 



In this paper, we prove that there is a canonical homotopy (n+1)algebra structure on the shifted operadic deformation complex $\Def(e_n\to\mathcal{P})[n]$ for any operad $\mathcal{P}$ and a map of operads $f\colon e_n\to\mathcal{P}$. This result generalizes a result of Tamarkin, who considered the case $\mathcal{P}=\End_\Op(X)$. Another more computational proof of the same result was recently sketched by Calaque and Willwacher. Our method combines the one of Tamarkin, with the categorical algebra on the category of symmetric sequences, introduced by Rezk and further developed by KapranovManin and Fresse. We define suitable deformation functors on ncoalgebras, which are considered as the "noncommutative" base of deformation, prove their representability, and translate properties of the functors to the corresponding properties of the representing objects. A new point, which makes the method more powerful, is to consider the argument of our deformation theory as an object of the category of symmetric sequences of dg vector spaces, not as just a single dg vector space . 
 
Language 



English
 
Source (journal) 



Theory and applications of categories.    
Publication 



2018
 
ISSN 



1201561X
 
Volume/pages 



33:32(2018), p. 9881030
 
Full text (open access) 


  
