From mboxrd@z Thu Jan  1 00:00:00 1970
X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4152
Path: news.gmane.org!not-for-mail
From: selinger@mathstat.dal.ca (Peter Selinger)
Newsgroups: gmane.science.mathematics.categories
Subject: Re: Cartesian closed without products
Date: Tue, 8 Jan 2008 21:36:39 -0400 (AST)
Message-ID: <E1JCkF5-0001O9-TU@mailserv.mta.ca>
NNTP-Posting-Host: main.gmane.org
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
X-Trace: ger.gmane.org 1241019755 11945 80.91.229.2 (29 Apr 2009 15:42:35 GMT)
X-Complaints-To: usenet@ger.gmane.org
NNTP-Posting-Date: Wed, 29 Apr 2009 15:42:35 +0000 (UTC)
To: categories@mta.ca
Original-X-From: rrosebru@mta.ca Wed Jan  9 19:34:05 2008 -0400
Return-path: <cat-dist@mta.ca>
Envelope-to: categories-list@mta.ca
Delivery-date: Wed, 09 Jan 2008 19:34:05 -0400
Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61)
	(envelope-from <cat-dist@mta.ca>)
	id 1JCkF5-0001O9-TU
	for categories-list@mta.ca; Wed, 09 Jan 2008 19:21:51 -0400
Original-Sender: cat-dist@mta.ca
Precedence: bulk
X-Keywords: 
X-UID: 13
Original-Lines: 24
Xref: news.gmane.org gmane.science.mathematics.categories:4152
Archived-At: <http://permalink.gmane.org/gmane.science.mathematics.categories/4152>

Toby Bartels wrote:
>
> Richard Garner wrote:
>
> >On reflection, [...]
> >EK-closed requires the unit object to be representable as
> >well.
>
> This is a reasonable requirement anyway,
> since the unit is the 0fold iterated hom,
> just as it's the 0fold iterated product.
> So if you think <closed under binary products>
> should be accompanied by <with a unit object>,
> then so should <closed under internal homs>.
>
> OTOH, the version without unit probably has some use,
> just as non-monoid semigroups occasionally do.

What is the "0fold iterated" of a non-associative operation?

-- Peter