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| ``Re: Category of Sets, according to MacLane''
by jkauzlar on 2008-06-11 22:30:29 |
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| Thank you. That makes it clearer, and I think something of this nature should be added to the article, since its not obvious (that is, to me, and I don't think I'm a lot dumber than most who are new to category theory).
In addition, the texts I looked at don't make it especially clear why, if the arrows represent morphisms between objects (sets), then why every set doesn't point to every other set (making every object both initial and terminal). I presume there is a hidden restriction that an arrow's codomain can't be a subset of the target, i.e. an arrow can't point from a set to a larger set, but it can point to a smaller set where the codomain is smaller.
I can only make assumptions like this (possibly false) at this point, because, like in MacLane, most texts are vague in this definition.
I would like to see an article that makes the structure of Set clear to a person who is only just learning about the category of sets.
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