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| ==== Discussion ==== | ==== Discussion ==== | ||
| - | ${\bf Cat}$ is the archetypical example for what is called a 2-cateogry: Each hom-class ${\bf Cat}[{\bf C},{\bf D}]$ is again a category. (More precisely, each hom-class of a 2-category is a 1-category.) | + | === Elaboration === |
| + | ${\bf Cat}$ is the archetypical example for what is called a 2-cateogry: Each hom-class ${\bf Cat}[{\bf C},{\bf D}]$ is again a (ordinary) category. | ||
| - | == Predicates == | + | Specifically, in ${\bf Cat}$, the hom-classes are functor categories and the hom-classes of those are natural transformations. |
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| + | === Predicates === | ||
| | @#EEEE55: predicate | @#EEEE55: ${\bf C}$ ... small $\equiv {\bf C}$ in ${\bf Cat}$ | | | @#EEEE55: predicate | @#EEEE55: ${\bf C}$ ... small $\equiv {\bf C}$ in ${\bf Cat}$ | | ||
