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Rotwang
Posts:
1,679
From:
Swansea
Registered:
7/26/06


Re: The Monoid Category in DC Proof
Posted:
Nov 9, 2012 4:03 PM


On 09/11/2012 20:56, Jesse F. Hughes wrote: > Rotwang <sg552@hotmail.co.uk> writes: >> [...] >> >> Sure. In fact this is what I was getting at with my "this is not a >> coincidence" comments  that the map that sends an element of a monoid >> to its left action is part of a functor from the monoid (considered a >> category) to Set. More generally, if C is any small category then the >> Yoneda functor C > Set^{C^{op}}, followed by the functor that takes F: >> C^{op} > Set to the coproduct of F(a) for a in ob(C), is a faithful >> functor from C to Set, which shows that any small category is >> concretizable. In the case where C has a single object this simplifies >> to the construction you give above. > > Ugh. > > Don't mention Yoneda to me, dammit. I'm pretty sure that's a part of > category theory which I've repressed. > > Though thanks for the result. If I've ever known it, I've forgotten it.
I can't take credit, I found it on Wikipedia.
 I have made a thing that superficially resembles music:
http://soundcloud.com/eroneity/weberatedourowncrapiness



