From: "Hans-Peter Stricker" <stricker@epublius.de>
To: "Aleks Kissinger" <aleks0@gmail.com>, <categories@mta.ca>
Subject: Re: Examples for the Yoneda lemma
Date: Fri, 15 Jan 2010 13:50:20 +0100 [thread overview]
Message-ID: <E1NVvVn-0003zJ-8e@mailserv.mta.ca> (raw)
In-Reply-To: <46ffa45f1001150307r793d81c6s7963324885fba107@mail.gmail.com>
Hello Aleks,
I am not quite what to think of the poset of unlabeled graphs without
isolated vertices with the relation of embeddability: I have the feeling,
that such a graph is NOT completely determined by its set of in-arrows (see
http://epublius.de/Fragment_of_the_category_of_unlabeled_graphs_without_isolated_vertices.pdf
to see what I mean, e.g. vertices 3 and 4 or vertices 7,8,9).
Do I miss something?
Best
Hans-Peter
----- Original Message -----
From: "Aleks Kissinger" <aleks0@gmail.com>
To: "Hans-Peter Stricker" <stricker@epublius.de>
Cc: <categories@mta.ca>
Sent: Friday, January 15, 2010 12:07 PM
Subject: Re: categories: Examples for the Yoneda lemma
> The simplest example I can think of is posets. If you represent a
> poset as a category (i.e. a category with at most one arrow from A->B
> such that A->B and B->A implies A=B), then an object A is completely
> determined by the set of arrows going in to it.
>
> In this context, the Yoneda embedding is the familiar result that any
> poset P embeds fully and faithfully in the powerset of P, ordered by
> subset inclusion.
>
>
> Aleks
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-01-15 12:50 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-01-15 0:24 Hans-Peter Stricker
2010-01-15 3:57 ` Steve Lack
2010-01-15 4:45 ` Vaughan Pratt
2010-01-15 11:07 ` Aleks Kissinger
[not found] ` <46ffa45f1001150307r793d81c6s7963324885fba107@mail.gmail.com>
2010-01-15 12:50 ` Hans-Peter Stricker [this message]
[not found] ` <E97707B8557E49B5B2FF24D048FCF54C@YOLATENGO>
2010-01-15 13:01 ` Aleks Kissinger
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