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The opening paragraph of the “cubical set - exposition” page states:
a cubical set is a space characterized by the fact that and how it may be probed by mapping standard cellular cubes into it
Is there text missing between “the fact that” and “and how”? Or is it supposed to say “by the fact that it may be probed”?
It may be probed by cubes and it comes with a prescription for how to probe it by cubes.
So something like
a cubical set is a space characterized by the fact that, and ways in which, it may be probed by mapping standard cellular cubes into it
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