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# categorical diagrams as functors

# 0.1 Introduction: categorical diagrams defined by functors

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.

# 0.2 Examples

Consider a scheme $\Sigma$ as defined in ref. [1]. Then one has the following short list of important examples of diagrams and functors:

1. Diagrams of adjoint situations: Adjoint functors

2. 3. Natural equivalence diagrams

4. Diagrams of natural transformations

5. Category of diagrams and 2-functors

6.

# References

- 1
Barry Mitchell.,
*Theory of Categories.*, Academic Press: New York and London (1965), pp.65-70.

## Mathematics Subject Classification

18E05*no label found*18D35

*no label found*18-00

*no label found*

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