Re: Examples for the Yoneda lemma

[Aleks Kissinger <aleks0@gmail.com>]

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

On Fri, Jan 15, 2010 at 12:24 AM, Hans-Peter Stricker
<stricker@epublius.de> wrote:
> Hello,
>
> I am looking for (simple) instructive examples for the Yoneda lemma, showing
> how to get the "inner" structure of an object from its morphisms. I've been
> told how to get a graph G from its morphisms (from the one-vertex-graph V to
> G and the one-edge-graph E to G and the morphisms from V to E) and
> appreciated this example a lot. Are there others equally simple and
> enlightening?
>
> What I wonder is which morphisms are definitely needed. In the graph example
> it's the morphisms from V -> G, E -> G and V -> E? Can this be abstracted
> and generalized?
>
> Many thanks in advance
>
> Hans-Stricker
>

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