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1. • CommentRowNumber1.
   • CommentAuthordomenico_fiorenza
   • CommentTimeOct 5th 2012
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   Author: domenico_fiorenza
   Format: MarkdownItexA matter of naming: how is the category whose objects are morphisms in a category $C$ and whose morphisms are commutative diagrams called? and which is the nLab page dedicated to it (that's why I need the name :) )

   A matter of naming: how is the category whose objects are morphisms in a category $C$ and whose morphisms are commutative diagrams called? and which is the nLab page dedicated to it (that’s why I need the name :) )

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeOct 5th 2012
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   Author: Todd_Trimble
   Format: MarkdownItexI generally call $C^\to$ the [[arrow category]].

   I generally call $C^\to$ the arrow category.

3. • CommentRowNumber3.
   • CommentAuthordomenico_fiorenza
   • CommentTimeOct 5th 2012
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   Author: domenico_fiorenza
   Format: MarkdownItexThanks! I guess that immediately generalizes to higher categories, despite the nLab page currently does not discuss this. In particular I'm interested into some sort of category having functors from $C\to D$ as objects and commutative diagrams (including the datum of a natural transformation between the two ways of going from the upper-left to the lower-right corner) as morphisms.

   Thanks! I guess that immediately generalizes to higher categories, despite the nLab page currently does not discuss this. In particular I’m interested into some sort of category having functors from $C\to D$ as objects and commutative diagrams (including the datum of a natural transformation between the two ways of going from the upper-left to the lower-right corner) as morphisms.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeOct 5th 2012
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   Author: Urs
   Format: MarkdownItexYou should look under [[category of functors]] and [[(infinity,1)-category of (infinity,1)-functors]] for that arrow category is $Func(\Delta^1, C)$. I'll try to add some more cross-links to the relevant nLab entries.

   You should look under category of functors and (infinity,1)-category of (infinity,1)-functors for that arrow category is $Func(\Delta^1, C)$.

   I’ll try to add some more cross-links to the relevant nLab entries.