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For large documents I tend to use \input{chapterX.tex} for, say, each chapter. In TexShop, is it possible to latex from, say, chapterX.tex instead of the master file? This is possible for instance in auctex. I couldn't find this in the documentation.

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Yes, it is possible. At the top of your chapterX.tex, include the following line:

%!TEX root = main.tex

where main.tex is the main file that has the \input{chapterX.tex} line. When you next open chapterX.tex, it will also open main.tex. When you hit Typeset at chapterX.tex, the focus will switch to main.tex and it will run latex on that file.

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