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Topic: Category theory (was Re: Consciousness, again)
Replies: 2   Last Post: Jun 16, 1996 2:21 PM

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Michael Weiss

Posts: 49
Registered: 12/6/04
Re: Category theory (was Re: Consciousness, again)
Posted: Jun 14, 1996 4:18 PM
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Matthew P Wiener writes:

Part of the difficulty is convincing yourself that you have made the
correct geometrical dissection. In 2 and 3 dimensions, you can just
look at the diagram and "know" you have it correct.

As an elementary problem of this sort, give a concrete geometrical
proof that homotopy induces equality in singular homology. The basic
difficulty [is to find a dissection of a prism into simplices]. But
cranking out the explicit description, and proving that it works, in
terms of all the basic definitions, is a wee bit of a mess.

I seem to recall a slick (but unmotivated) trick around this, called
the method of cyclic models. Can one do something similar in the
n-category case?







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