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In homological algebra, the snake lemma, a statement valid in every abelian category, is the crucial tool used to construct the long exact sequences.
A natural transformation, as a morphism between functors, respects the "functor structure". This idea, as usual in category theory, is expressed in a commutative diagram, pictured on the right.
In category theory, a limit of a diagram is defined as a cone satisfying a universal property. Products and equalizers are special cases of limits. The dual notion is that of colimit.
