Statement
In an abelian category (such as the category of abelian groups or the category of vector spaces over a given field), consider a commutative diagram:
where the rows are exact sequences and 0 is the zero object. Then there is an exact sequence relating the kernels and cokernels of a, b, and c:
Furthermore, if the morphism f is a monomorphism, then so is the morphism ker a → ker b, and if g' is an epimorphism, then so is coker b → coker c.
Read more about this topic: Snake Lemma
Famous quotes containing the word statement:
“After the first powerful plain manifesto
The black statement of pistons, without more fuss
But gliding like a queen, she leaves the station.”
—Stephen Spender (1909–1995)
“Eloquence must be grounded on the plainest narrative. Afterwards, it may warm itself until it exhales symbols of every kind and color, speaks only through the most poetic forms; but first and last, it must still be at bottom a biblical statement of fact.”
—Ralph Waldo Emerson (1803–1882)
“A sentence is made up of words, a statement is made in words.... Statements are made, words or sentences are used.”
—J.L. (John Langshaw)