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• CommentRowNumber1.
• CommentAuthorEric
• CommentTimeNov 3rd 2009

I created cone morphism and immediately realized I needed help.

I thought it was cool when I finally understood it after staring at it a few times at Understanding Constructions in Set. However, my understanding is in terms of objects and components of cones, but there is probably some slick way to define it all in one fell swoop.

• CommentRowNumber2.
• CommentAuthorEric
• CommentTimeNov 3rd 2009

I managed to straighten out some of the initial mess, but would still be interested in a "component free" definition as a supplement to what is there (if possible).

I added a bit about "pulling back" cones, which probably needs blessing so that I can remove the "tentative" warning.

• CommentRowNumber3.
• CommentAuthorFinnLawler
• CommentTimeNov 3rd 2009

• CommentRowNumber4.
• CommentAuthorEric
• CommentTimeNov 4th 2009

Thanks Finn. I think I understand what you were trying to tell me now and added a statement "whose component is $\phi:c\to c'$" to the definition (although it was probably obvious). Thanks again!

• CommentRowNumber5.
• CommentAuthorFinnLawler
• CommentTimeNov 4th 2009

No problem, Eric. I edited the page a bit to try to clarify the point that you've just grokked.

• CommentRowNumber6.
• CommentAuthorEric
• CommentTimeNov 4th 2009

Beautiful!

By the way, where you say $i,j\in C$, should that be $i,j\in J$? Just checking...

• CommentRowNumber7.
• CommentAuthorFinnLawler
• CommentTimeNov 5th 2009

Yes, typo -- well spotted. Fixed.