A colleague can fetch from, but not push to a remote repository. I suspect that he has only read and not write permissions on the remote. There are various ways I can check this but I cannot think of one he can use within git.
Is there a git command to show one's permissions on a given remote repository?
No.
Git doesn't handle any permission mechanism itself. One of the reason he can not push is he doesn't have the right access on the remote filesystem.
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