Last Updated：2025/11/26

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(mathematics, somewhat informal) Proof in stages, each of which, in general, depends on the previous stages and can be visualized by means of a diagram of morphisms.

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diagram chasing

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Source Word

diagram chasing

Noun

informal uncountable

(mathematics, somewhat informal) Proof in stages, each of which, in general, depends on the previous stages and can be visualized by means of a diagram of morphisms.

Japanese Meaning

（数学、やや口語）各段階の証明が前段階に依存する形で進む証明手法。射（morphisms）の図を使ってその証明過程を視覚化する方法。

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The students used diagram chasing to verify exactness at each step of the long exact sequence.

Google Translation / DeepL Translation

学生たちは、長い完全列の各段階で完全性を確認するために図追跡を用いた。

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(mathematics, somewhat informal) Proof in stages, each of which, in general, depends on the previous stages and can be visualized by means of a diagram of morphisms.

Category theory also contributes new proof techniques, such as diagram chasing or arguments by duality; Steenrod called these methods “abstract nonsense.”³ The aim of this text is to introduce the language, philosophy, and basic theorems of category theory. A complementary objective is to put this theory into practice: studying functoriality in algebraic topology, naturality in group theory, and universal properties in algebra.

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diagram chasing

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