Diagram chasing is a method of mathematical proof used especially in homological algebra. Given a commutative diagram, a proof by diagram chasing involves the formal use of the properties of the diagram, such as injective or surjective maps, or exact sequences. A syllogism is constructed, for which the graphical display of the diagram is just a visual aid. It follows that one ends up "chasing" elements around the diagram, until the desired element or result is constructed or verified.
Examples of proofs by diagram chasing include those typically given for the five lemma, the snake lemma, the zig-zag lemma, and the nine lemma.
Read more about this topic: Commutative Diagram
Famous quotes containing the words diagram and/or chasing:
“If a fish is the movement of water embodied, given shape, then cat is a diagram and pattern of subtle air.”
—Doris Lessing (b. 1919)
“We like the chase better than the quarry.... And those who philosophize on the matter, and who think men unreasonable for spending a whole day in chasing a hare which they would not have bought, scarce know our nature. The hare in itself would not screen us from the sight of death and calamities; but the chase, which turns away our attention from these, does screen us.”
—Blaise Pascal (1623–1662)