From: Thorsten Palm <palm@iti.cs.tu-bs.de>
To: David Spivak <dspivak@gmail.com>
Cc: categories list <categories@mta.ca>
Subject: Re: question about discrete op-fibrations
Date: Thu, 2 Feb 2012 11:22:56 +0100 (MET) [thread overview]
Message-ID: <E1Rt95F-0003hX-Cl@mlist.mta.ca> (raw)
In-Reply-To: <E1RsasQ-0002zc-9d@mlist.mta.ca>
David Spivak hat am 31.01.12 geschrieben:
>
> Let DOF denote the category whose objects are small categories C,D,
> etc. and in which Hom(C,D) is the set of discrete op-fibrations C-->D.
> For a category C, let DOF_{C/} denote the coslice over C.
>
> Question: Does there exist a terminal object in DOF_{C/}?
Answer: No.
The "op-" is irrelevant; let us look at DF_{C/} instead. There is not
even a weakly terminal object, for the same reason for which there
isn't one in DF itself. (Suppose (T,z) is one. Let A be an arbitrary
small category having a terminal object a. From the object (C+A,incl)
of DF_{C/} we get a discrete fibration f : A-->T. But then for t =
f(a) the slice category T_{/t} is isomorphic to A. There are not
enough t to accommodate all possible A.)
Thorsten Palm
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
prev parent reply other threads:[~2012-02-02 10:22 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2012-02-01 0:03 David Spivak
2012-02-01 23:29 ` Mark Weber
[not found] ` <81982979-2217-4AC4-AEDD-154DB2EEAC7B@gmail.com>
2012-02-02 5:51 ` David Spivak
2012-02-03 14:07 ` Thorsten Palm
2012-02-02 10:22 ` Thorsten Palm [this message]
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