Fixed definition 2.4.

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

]]>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.

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

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

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 ?

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

]]>Thanks Harry. That's what I thought. So and mean the same thing.

]]>Edit: Changed this comment to a question.

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

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

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

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