Yes. The Authorea editor supports all major shortcuts that you expect in a modern browser, such as:
Ctrl-z (⌘-z) to Undo Typing
Ctrl-c + Ctrl-v (⌘-c + ⌘-v) to Copy and Paste Text
Tab to indent Text

Latex and Markdown. When writing LaTeX and Markdown snippets, you can use many additional shortcuts for writing (full list). You can even customize your editor to use Emacs or VIM key bindings. In order to do so, navigate to User Settings and under Editor Preferences, set Keybinding to "Emacs" or "vim".

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