#
$A_\infty$-morphisms with several entries

##
Volodymyr Lyubashenko

We show that morphisms from n $A_\infty$-algebras to a single one are
maps over an operad module with n+1 commuting actions of the operad
$A_\infty$, whose algebras are conventional $A_\infty$-algebras. The
composition of $A_\infty$-morphisms with several entries is presented as
a convolution of a coalgebra-like and an algebra-like structures. Under
these notions lie two examples of Cat-operads: that of graded modules and
of complexes.

Keywords:
$A_\infty$-algebra, $A_\infty$-morphism, multicategory, multifunctor,
operad, operad module, polymodule cooperad

2010 MSC:
18D50, 18D05, 18G35

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 45, pp 1501-1551.

Published 2015-11-05.

http://www.tac.mta.ca/tac/volumes/30/45/30-45.pdf

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