From: soloviev@irit.fr
To: "David Leduc" <david.leduc6@googlemail.com>
Cc: categories@mta.ca
Subject: Re: product for free
Date: Wed, 18 Aug 2010 08:18:54 +0200 (CEST) [thread overview]
Message-ID: <E1Om2t8-0008LA-4Y@mlist.mta.ca> (raw)
In-Reply-To: <E1OlX3J-0000O9-18@mlist.mta.ca>
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 ≡ λx.λy.λz.z x y
> fst ≡ λp.p (λx.λy.x)
> snd ≡ λp.p (λx.λy.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:[~2010-08-18 6:18 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 [this message]
2010-08-20 2:16 ` Robert Seely
2010-08-18 14:36 ` Rasmus Møgelberg
2010-08-19 12:59 ` Gordon Plotkin
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