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As seen in this github issue, Xcode does not seem to create a symlink for MacOSX11.1.sdk, so Homebrew fails to install anything. I'm sure Homebrew isn't be the only program failing to build code because of this error.

The solution would be to reinstall the Command-line Tools or create these symlinks yourself if reinstalling doesn't fix it:

Code Block
ln -s /Applications/ /Applications/

Code Block
ln -s /Library/Developer/CommandLineTools/SDKs/MacOSX11.0.sdk /Library/Developer/CommandLineTools/SDKs/MacOSX11.1.sdk

Note: This is only a temporary fix to get builds affected by this issue working again, however it may break the SDK in some unknown ways.
Up vote post of rotwhiter