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The phrase "a category error" is correct and usable in written English.
It can be used when discussing a mistake in logic or reasoning where a concept is applied to a category to which it does not belong.
Example: "Claiming that a computer can be happy is a category error, as happiness is a human emotion."
Alternatives: "a classification mistake" or "a conceptual error".
Exact(46)
They suffer from a category error.
But it is a category error.
Blaming the EU was a category error.
It's based on a category error.
"Suicide Squad" is the victim of a category error.
That does seem to be a category error.
Similar(14)
But on the plus side they have bedrooms you can smoke in, and frankly, I'm one of those writers who smokes — indeed, for me to sit in a room typing and not smoke would be a grotesque category error, akin to a bear tidily using a restroom.
To some, it seems like a monumental category error, like giving the Man Booker to, say, an oral poet.
There's a fundamental category error endemic to criticism: the notion that there's an arm's-length appreciation of craft that's somehow secondary to the principal business of a movie, the creation of character, the unfolding of drama.
This really is a bizarre category error.
This book's subtitle contains of course a fundamental category error.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com