Any categorical diagram can be defined via a corresponding functor (associated with a diagram as shown by Mitchell, 1965, in ref. [1]). Such functors associated with diagrams are very useful in the categorical theory of representations as in the case of categorical algebra. As a particuarly useful example in (commutative) homological algebra let us consider the case of an exact categorical sequence that has a correspondingly defined exact functor introduced for example in abelian category theory.
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