Selectable is an option for boxes, cells and notebooks which specifies whether their contents can be selected interactively using the front end.
Even with the setting Selectable->False, an object can be selected as a whole.
With Selectable->False set at the notebook level, no cells in the notebook can be selected.
See the Mathematica book: Section 2.8.10, Section 2.10.9.
See also: Editable, WindowClickSelect, StructuredSelection.
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