Developing a gitlab application. How do applications work across domains?

Hello, first time posting!

I am developing an web application using gitlabs api that captures data around a OAuth User’s account. Once they log in, it captures groups, projects, commits, members info and displays interesting metrics. I currently have the OAuth/API for my universities instance of GitLab. ie.

I was wondering if applications can be developed agnostic to domain? IE. the application can be used by any domain, as long as the user enters it. Will the OAuth only work with the domain that was develop in?

I can’t find any info in the docs, so guidance on this matter would be appreciated!