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arXiv · 1205.6072

A_infinity-morphisms with several entries

Volodymyr Lyubashenko
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Abstract

We show that morphisms from n A_infinity-algebras to a single one are maps over an operad module with n+1 commuting actions of the operad A_infinity, whose algebras are conventional A_infinity-algebras. Similar statement holds for homotopy unital A_infinity-algebras. The operad A_infinity and modules over it have two useful gradings related by isomorphisms which change the degree. The composition of A_infinity-morphisms with several entries is presented as a convolution of a coalgebra-like and an algebra-like structures. For this sake notions of lax Cat-span multicategories and multifunctors are introduced. They are lax versions of strict multicategories and multifunctors associated with the monad of free strict monoidal category.

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Volodymyr Lyubashenko. 2012-05-28. A_infinity-morphisms with several entries. https://arxiv.org/abs/1205.6072

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