From: Robert Seely <rags@math.mcgill.ca>
To: soloviev@irit.fr
Cc: David Leduc <david.leduc6@googlemail.com>, categories@mta.ca
Subject: Re: product for free
Date: Thu, 19 Aug 2010 22:16:06 -0400 (EDT) [thread overview]
Message-ID: <E1OmLpc-0003s8-03@mlist.mta.ca> (raw)
In-Reply-To: <E1Om2t8-0008LA-4Y@mlist.mta.ca>
More to the point, it is a "weak product" (lacking the uniqueness
condition one usually has) - I think this is discussed in Lambek
Scott, but am away from my library to verify this ...
-= rags =-
On Wed, 18 Aug 2010, soloviev@irit.fr wrote:
> Remark:
>
> as far as I remember, one need to be cautios
> calling this a product, because ordinary product
> equations do not hold with this definition and
> standard equality of lambda-calculus.
>
> Best wishes
>
> Sergei Soloviev
>
>> Hi,
>>
>> In lambda-calculus one can define the product of types A and B by:
>>
>> forall C, (A->B->C)->C.
>>
>> with pairing and projections defined as:
>>
>> pair ÿÿ ÿÿx.ÿÿy.ÿÿz.z x y
>> fst ÿÿ ÿÿp.p (ÿÿx.ÿÿy.x)
>> snd ÿÿ ÿÿp.p (ÿÿx.ÿÿy.y)
>>
>> What would be the equivalent in a closed monoidal category?
>> Would we get a product for free?
>>
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next prev parent reply other threads:[~2010-08-20 2:16 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-08-17 13:27 David Leduc
2010-08-18 6:18 ` soloviev
2010-08-20 2:16 ` Robert Seely [this message]
2010-08-18 14:36 ` Rasmus Møgelberg
2010-08-19 12:59 ` Gordon Plotkin
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