Extension of the Multiplication Operation in E_∞-Algebras to an A_∞-Morphism of E_∞-Algebras and Cartan Objects in the Category of May Algebras

摘要

It is proved in the paper that the multiplication operation on an arbitrary E_∞ -algebra can be extended to an E_∞-algebra A_∞-morphism. As a corollary, it is proved that every May algebra defined by an E_∞-algebra is a Cartan object in the category of May algebras.