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> It turns out that the usual categorical semantics for linguistics shares a lot with the categorical semantics for quantum mechanics

so?

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One other thing that has a lot in common with those two is algebraic data types. Products and sums crop up in all these areas. Maybe it's enough to say that with category theory, we feel like we are revealing the "elementary particles" (or rules) of all of these systems.

Type theory has also been applied to both linguistics and quantum mechanics.

What does it mean that both category theory and type theory have been applied to both linguistics and quantum mechanics?

"categorical semantics for linguistics" gives 0 hits in Google btw.

"categorical semantics for quantum mechanics" gives 5 hits all of which reference the same paper by Bob Coecke titled “Strongly Compact Closed Semantics”, which uses the phrase only once.

I'm showing 1M and 200K Google results for those phrases, respectively.

Those exact phrases? In quotation marks?

No, those result numbers do not include quotation marks. With the quotes I show the same results as you.

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