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Math Forum » Discussions » sci.math.* » sci.math.research

Topic: Concretizable categories
Replies: 9   Last Post: Apr 11, 2006 10:30 AM

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Colin McLarty

Posts: 11
Registered: 3/3/06
Re: Concretizable categories
Posted: Apr 6, 2006 8:56 AM
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The proof is Freyd's. I think it is fair to summarize the idea this
way: Think of how every contractible space is a mere singleton, a
terminal object, in the homotopy category, while a proper class of
homotopically different spaces are quotients of contractible spaces.
The terminal object has a proper class of different quotients. Indeed
every object in the homotopy category has a proper class of different
quotients, and so the category cannot be concrete.

In fact the result is very sensitive to which homotopy category you
take. It is much more subtle than this version. But I think that is
the core idea.

Colin

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