Can the real time operating system used in aviation equipment be certified by itself? Can the real time operating system used in aviation equipment be certified by itself, or must it be a part of some software certification effort?

I'm asking for getting a certificate of 178C. I don't understand if it is possible. There are a lot of resources that tell us about "certified operating system", but if is certified as a part of a project or it is certified just itself without any project... I have no practise in this field, but I was asked this question and it makes me puzzled.
A DO-178C compliant RTOS (such as LynxOS-178 mentioned by @mins) is going to have a certification package you provide along with your DO-178C artifacts for your software.

Note that there is no such thing as a DO-178C "certificate". DO-178C is a process that generates certification artifacts that are packaged and provided to the Certification Authority as part of some approval application (TSO, TC, STC, PMA)

It is also usefull to recognize that most software on equipment installed on an aircraft is not going to run on an RTOS, but rather run directly on the hardware (bare metal)