50:. It states: if the diagram to the right is a commutative diagram and all columns as well as the two bottom rows are exact, then the top row is exact as well. Likewise, if all columns as well as the two top rows are exact, then the bottom row is exact as well. Similarly, because the diagram is symmetric about its diagonal, rows and columns may be interchanged in the above as well.
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board... Do not fill it in with noughts and crosses... Instead, use curved arrows... Wave your hands about in complicated patterns over this board. Make some noughts, but not in the squares; put them at both ends of the horizontal and vertical lines. Make faces. You have now proved:
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61:(to the two bottom rows in the first case, and to the two top rows in the second case).
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113:(Repr. of 1. ed. 1963. ed.). Berlin : Springer. pp. 365–366.
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64:
Linderholm (p. 201) offers a satirical view of the nine lemma:
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16:Category theory lemma about commutative diagrams
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92:(see Lemmas 3.3, 3.4 in Chapter XII of ).
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53:The nine lemma can be proved by direct
84:There are two variants of nine lemma:
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34:(or 3×3 lemma) is a statement about
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1:
80:(c) the Twenty-five Lemma...
185:
136:Mathematics Made Difficult
109:MacLane, Saunders (1967).
169:Lemmas in category theory
133:Linderholm, Carl (1971).
42:valid in the category of
82:
23:
78:(b) the Sixteen Lemma
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57:, or by applying the
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90:symmetric nine lemma
36:commutative diagrams
164:Homological algebra
70:noughts-and-crosses
76:(a) the Nine Lemma
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86:sharp nine lemma
48:abelian category
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55:diagram chasing
40:exact sequences
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59:snake lemma
28:mathematics
158:Categories
96:References
32:nine lemma
139:. Wolfe.
111:Homology
46:and any
68:Draw a
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44:groups
30:, the
141:ISBN
115:ISBN
88:and
38:and
26:In
160::
149:.
123:.
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