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We construct a configuration space model for a particular 2-coloreddifferential graded operad encoding the structure of two $A_\infty$ algebraswith two $A_\infty$ morphisms and a homotopy between the morphisms. Thecohomology of this operad is shown to be the well-known 2-colored operadencoding the structure of two associative algebras and of an associativealgebra morphism between them.

Compactified configuration space of points on a line and homotopies of $A_\infty$ morphisms