notation. string diagrams: category, object and arrow [marsden2014category, sec. 2.1] [tt-0004]

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Later, when we have learned about functors and natural transformations, we will see that, in string diagram for 1-category:

1. A category \({\cal C}\) is represented as a colored region:
2. Functors of type \(\mathbf {1} \to {\cal C}\) can be identified with objects of the category \({\cal C}\), where \(\mathbf {1}\) is the the terminal category, so an object \(X \in \operatorname {Ob}({\cal C})\) can be represented as:
3. An arrow \(f : X \to Y\) is then a natural transformation between two of these functors, represented as: