Lots of examples in http://boole.stanford.edu/pub/yon.pdf . It's an 18-page paper, yet already by page 2 there are six examples, none of them the usual graph example. In coming to grips with those examples it is *very* helpful to realize that every algebraic theory including the well-known ones having at least one constant or constant operation has a unary subtheory obtained by fixing all but one argument of every nonzeroary operation in the clone (which will be just projection if and only if all nonzeroary operations are projections). And while you don't need it on page 2, further on it is helpful to realize that for every algebraic theory, its models form a full subcategory of a presheaf category. In order to reach a broader audience the paper was written for an algebraic audience. If you're more familiar with category language than algebraic language a little adaptation will be needed. Let me know if translating back into category theory gives any trouble, this would be helpful feedback to have. Vaughan Pratt Hans-Peter Stricker 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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