Category-theoretic generality that encompasses a formalism does not constitute the kind of scientific indispensability that warrants treating inconsistent theories as equally reasonable mathematical objects.

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Category theory(as used in mathematical logic): A highly abstract branch of mathematics that studies how different mathematical structures relate to and transform into each other, rather than focusing on the structures themselves.
Inconsistent theories(as used in logic and philosophy of science): Sets of ideas or rules that contradict each other—where one part says something is true and another part says it's false.
Mathematical objects(as used in philosophy of mathematics): Abstract things that mathematicians study, like numbers, shapes, or functions—they don't exist in the physical world, only in our minds and on paper.
Scientific indispensability(in philosophy of science): The idea that something is so necessary and useful for doing science that we have good reason to believe it's real or true.

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