The snake lemma is a diagram lemma stating that the above commutative diagram of Abelian
groups and group homomorphisms whose rows
are exact sequences gives rise to an exact
sequence
This commutative diagram shows how the first commutative diagram (shown here in blue) can
be modified to exhibit the long exact sequence
(shown here in red) explicitly. The map 
is called a connecting
homomorphism and describes a curve from the end of
the upper row (
)
to the beginning of the lower row (
), which suggested the name given
to this lemma.
The snake lemma is explained in the first scene of Claudia Weill's film It
Is My Turn (1980), starring Jill Clayburgh and Michael Douglas.
See also
Commutative Diagram,
Connecting Homomorphism,
Diagram Lemma,
Exact
Sequence
Portions of this entry contributed by Margherita
Barile
Portions of this entry contributed by Christopher
Stover
Explore with Wolfram|Alpha
References
Bourbaki, N. "Le diagramme du serpent." §1.2 in Algèbre, Ch. 10: Algèbre Homologique. Paris, France:
Masson, pp. 3-7, 1980.The Internet Movie Database. "Memorable
Quotes from It Is My Turn." http://us.imdb.com/Quotes?0080936.Lang,
S. Algebra,
rev. 3rd ed. New York: Springer-Verlag, pp. 158-159, 2002.Mac
Lane, S. Categories
for the Working Mathematician. New York: Springer-Verlag, pp. 202-204,
1971.Munkres, J. R. Elements
of Algebraic Topology. New York: Perseus Books Pub., p. 141, 1993.Referenced
on Wolfram|Alpha
Snake Lemma
Cite this as:
Weisstein, Eric W., with contributions by Margherita Barile and Christopher Stover. "Snake
Lemma." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SnakeLemma.html
Subject classifications
