Dependency Injection with EF - is mapping required?

I'm implementing the Repository pattern with using DI and EF6.

I created the database (that inherits from DbContext) object with the Visual Studio wizard ADO.NET Entity Data Model

I have a generic IRepository<T> in my domain assembly, and its implementation in different assemblies based on the data source.

The problems come with the mapping objects from the EF to the domain objects: almost all of my code is writing things like

private Sql.Database.Cat Map(Domain.Data.Cat cat)
{
    return new Sql.Database.Cat
    {
        Species = cat.Species,
        Legs = cat.Legs,
        ...
    }
}

and the opposite of course. The mapping creates a big amount of problems, eg updating, but it is necessary in order not to add the Sql.Database dll as a dependency in the UI assembly.

Is there a way not to have to map objects and not having the EF assembly as a dependency as well?