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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 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 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 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 .

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