When you say library, are you talking about a static library or a DLL?
In the latter case, the main two possibilites for C# are:
- use PInvoke can call exported static class member functions or regular function
- write a mixed-mode wrapper assembly in C++/CLI
When it comes to Objective C, this is outside of my skillset. But this thread suggests that you can use C-linkage but not C++, due to name mangling. So you'd need to expose your C++ functionality via a C API.