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💡 观点 / 杂谈

范畴论的迷思The mythology of category theory

johndcook.com·2026-05-06 节选正文

文章探讨范畴论在数学与计算机科学中的应用迷思,指出人们常误以为它能‘无中生有’地解决复杂问题。实际上,范畴论更多是描述模式的语言工具,而非万能解决方案。作者引用 Qiaochu Yuan 的观点,强调其价值在于组织思想,而非替代具体计算或证明。

John

Yesterday a friend and I had a conversation about category theory, how it can be a useful pattern description language, but also about how people have unrealistic expectations for it, believing category theory can deliver something for nothing.

Later I ran across the following post from Qiaochu Yuan. It felt as if he had overheard my conversation and summarized it in a tweet:

category theory is just some straightforwardly useful stuff for some purposes in some fields! you can elegantly simplify and streamline some proofs. then there is the mythology of category theory, which is some other thing entirely, mostly wishful thinking and projection afaict

His phrase “the mythology of category theory” gives a name to this idea that category theory can deliver specific outputs without specific inputs. It helps to distinguish CT as a scrapbook of patterns from CT as sorcery.

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