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Homotopy unital $A_\infty$-morphisms with several entries
Theory and applications of categories, Tome 30 (2015), pp. 1552-1623 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We show that morphisms from n homotopy unital $A_\infty$-algebras to a single one are maps over an operad module with n+1 commuting actions of the operad $A_\infty^\hu$, whose algebras are homotopy unital $A_\infty$-algebras. The operad $A_\infty$ and modules over it have two useful gradings related by isomorphisms which change the degree. The composition of $A_\infty^\hu$\n-morphisms with several entries is presented as a convolution of a coalgebra-like and an algebra-like structures.

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Classification : 18D50, 18D05, 18G35
Keywords: $A_\infty$-algebra, $A_\infty$-morphism, multicategory, multifunctor, operad, operad module, polymodule cooperad 
@article{TAC_2015_30_a45,
     author = {Volodymyr Lyubashenko},
     title = {Homotopy unital $A_\infty$-morphisms with several entries},
     journal = {Theory and applications of categories},
     pages = {1552--1623},
     year = {2015},
     volume = {30},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a45/}
}
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Volodymyr Lyubashenko. Homotopy unital $A_\infty$-morphisms with several entries. Theory and applications of categories, Tome 30 (2015), pp. 1552-1623. http://geodesic.mathdoc.fr/item/TAC_2015_30_a45/