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categories: Re: Addendum

To: categories@mta.ca
Subject: categories: Re: Addendum
From: Vaughan Pratt <pratt@cs.stanford.edu>
Date: Sun, 16 Jan 2000 22:37:40 -0800
In-reply-to: Your message of "Sat, 15 Jan 2000 13:07:11 EST." <200001151807.NAA10666@saul.cis.upenn.edu>
Sender: cat-dist@mta.ca


>               * | A  B
>               --+------
>               A | B  A
>               B | A  A
>
>The unique cubical coalgebra is  A  but there is no square coalgebra.
>
>What I don't have is a counterexample with an _associative_ bifunctor.

How about the positive integers with * as sum, with 1->3 as the only
nonidentity arrow?  The unique cubical coalgebra is  1  but there is no
square coalgebra.

Vaughan

Follow-Ups:
- categories: Re: Addendum
  - From: Vaughan Pratt <pratt@cs.stanford.edu>
- categories: Re: Addendum
  - From: "Dr. P.T. Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>

References:
- categories: Addendum
  - From: Peter Freyd <pjf@saul.cis.upenn.edu>

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