Dependency injection in cross cutting visual studio solution

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ASP.NET-Core

I am so much tidy with my application's solution and cross cutting solution. I have created an asp.net core API solution in VS 2017 and also have a cross cutting solution with multiple common projects accessible to my API solution's project. Now, I am resolving dependencies for my cross cutting projects' objects at runtime through my separate API solution.

Should I do this? because It's actually tightly binding my API solution and cross cutting solution.

Or any alternate way, to de-couple both of these? or should I create a dependency file for my cross cutting projects object but resolve where in API or in Cross cutting solution?

What I have tried:

I just have tried to initialized all objects in cross cutting area into their own constructors but some objects need to get information or configurations from API solution, so it's becoming interlinking with both these solution.