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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeApr 5th 2010

The minute before I had entered offline territory a few days ago, I had expanded the list of examples of (commuting) diagrams at diagram.

• CommentRowNumber2.
• CommentAuthorMike Shulman
• CommentTimeApr 6th 2010

I added a few more, and also improved (I hope) the introduction.

• CommentRowNumber3.
• CommentAuthorEric
• CommentTimeApr 6th 2010
• (edited Apr 6th 2010)

Edit: Changed this comment to a question.

Is $Quiv$ on diagram the category of free categories on graphs or is it the same thing as $DiGraph$ as defined on directed graph?

• CommentRowNumber4.
• CommentAuthorHarry Gindi
• CommentTimeApr 6th 2010
I just checked the page, and it means the non-John Baez version of quiver.
• CommentRowNumber5.
• CommentAuthorEric
• CommentTimeApr 6th 2010

Thanks Harry. That's what I thought. So $Quiv$ and $DiGraph$ mean the same thing.

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeOct 31st 2017

We had the definitions of limit and colimit as terminal and initial (co)cones round the wrong way, so have corrected at diagram.

• CommentRowNumber7.
• CommentAuthorwillymox
• CommentTimeJun 12th 2020

Hi I’m new here. First of all thanks for this great resource you all created. I think there might be a mistake in the component definition of a diagram here. Particularly in the definitions of limiting cone (limit) and limiting co-cone (co-limit). I think it should be stated that the limiting cone is initial among all possible cones and the limiting co-cone is terminal among all possible co-cone. Not the opposite. I might be wrong here, I’m just a hobbyist category theorist ;) Did I misunderstand something ?

• CommentRowNumber8.
• CommentAuthorTodd_Trimble
• CommentTimeJun 13th 2020

No, it’s right as it is, but I think I can understand why some might find it confusing.

Take a simple example, where diagrams are over a discrete category with just two objects. If the diagram consists of objects $X, Y$, then a general cone looks like

$\array{ A \\ \mathllap{f} \downarrow & \searrow \mathrlap{g} & \\ X & & Y }$

The limiting cone is the product $X \times Y$ together with its product projections:

$\array{ & & X \times Y \\ & \mathllap{\pi_1} \swarrow & \downarrow \mathrlap{\pi_2} \\ X & & Y }$

and for any cone as in the first diagram, there is a unique map of cones to the product cone, given by a map

$A \stackrel{(f, g)}{\to} X \times Y.$

Thus the product cone is terminal among all cones: terminal means that for any object there exists a unique map to the terminal.

• CommentRowNumber9.
• CommentAuthorwillymox
• CommentTimeJun 13th 2020
• (edited Jun 13th 2020)

So we agree, the definition should say it’s terminal, not initial like it is now : over this diagram (def. 2.3) which is universal or initial among all possible cones, in that it ... <– This is from the definition of a limiting cone in definition 2.4, it should say terminal instead of initial. Same for limiting co-cone.

• CommentRowNumber10.
• CommentAuthorTodd_Trimble
• CommentTimeJun 13th 2020

I see; I was looking at a different part of the page where it was correct. You’re right.

• CommentRowNumber11.
• CommentAuthorTodd_Trimble
• CommentTimeJun 13th 2020

Fixed definition 2.4.