A diagram lemma also known as commutative diagram illustrated above with
exact rows and columns can be completed by two morphisms
without losing commutativity.
Moreover, the short exact sequence
is exact.
The lemma is also true if the roles of the first and the third row are interchanged.
See also Commutative Diagram ,
Exact
Sequence
This entry contributed by Margherita
Barile
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References Mitchell, B. Theory of Categories. Mac
Lane, S. Homology. Referenced on Wolfram|Alpha Nine Lemma
Cite this as:
Barile, Margherita . "Nine Lemma." From MathWorld Eric
W. Weisstein . https://mathworld.wolfram.com/NineLemma.html
Subject classifications
lemma. According to its most general statement, the
commutative diagram illustrated above with
exact rows and columns can be completed by two morphisms
