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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