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This story was originally published on HackerNoon at: https://hackernoon.com/reexamining-canonical-isomorphisms-in-modern-algebraic-geometry.
A critical look at how mathematicians use the word “canonical,” revealing how informal shortcuts obscure the real constructions behind key theorems.
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The article examines how mathematicians casually label maps as “canonical,” why this obscures the constructive content of theorems like the first isomorphism theorem, and how formalizing algebraic geometry forces greater precision about what canonical truly means.
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