In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree p and q to form a composite cocycle of degree p + q. This defines an associative (and distributive) graded commutative product operation in cohomology, turning the cohomology of a space X into a graded ring, H∗(X), called the cohomology ring. The cup product was introduced in work of J. W. Alexander, Eduard Čech and Hassler Whitney from 1935–1938, and, in full generality, by Samuel Eilenberg in 1944.
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“The cup of blessing that we bless, is it not a sharing in the blood of Christ? The bread that we break, is it not a sharing in the body of Christ?”
—Bible: New Testament, 1 Corinthians 10:16.
“The writer’s language is to some degree the product of his own action; he is both the historian and the agent of his own language.”
—Paul De Man (1919–1983)