diagram chasing

English edit

diagram chasing (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.
- 2016, Emily Riehl, Category Theory in Context (Aurora: Dover modern math originals)‎^[1], New York: Dover, →ISBN, →OCLC, page x:
  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.
To prove the five lemma, just use diagram chasing.