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cat [2014/12/02 12:05]
nikolaj
cat [2014/12/02 12:09]
nikolaj
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 | @#55EE55: postulate ​  | @#55EE55: $\mathrm{Ob}_{\bf C},​\mathrm{Mor}_{\bf C} $ ... small | | @#55EE55: postulate ​  | @#55EE55: $\mathrm{Ob}_{\bf C},​\mathrm{Mor}_{\bf C} $ ... small |
 | @#FFFDDD: for all     | @#FFFDDD: ${\bf D}\in{\bf Cat}$ | | @#FFFDDD: for all     | @#FFFDDD: ${\bf D}\in{\bf Cat}$ |
-| @#55EE55: postulate ​  | @#55EE55: ${\bf Cat}[{\bf C},{\bf D}]$ ... functor category |+| @#55EE55: postulate ​  | @#55EE55: ${\bf Cat}[{\bf C},{\bf D}]$ ... functor category ​$({\bf C},{\bf D})$ |
  
 ==== 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. 
 + 
 +=== Predicates ​===
 | @#EEEE55: predicate ​  | @#EEEE55: ${\bf C}$ ... small $\equiv {\bf C}$ in ${\bf Cat}$ | | @#EEEE55: predicate ​  | @#EEEE55: ${\bf C}$ ... small $\equiv {\bf C}$ in ${\bf Cat}$ |
  
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 [[Locally small category]] ​ [[Locally small category]] ​
 === Requirements === === Requirements ===
-[[Set universe]]+[[Set universe]], [[Functor category]]
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