From: Jamie Vicary <jamievicary@gmail.com>
To: Categories list <categories@mta.ca>
Subject: Slick proof that f (x) (g+h) = (f (x) g) + (f (x) h) in a monoidal category with 0, biproducts and duals
Date: Fri, 11 Oct 2013 13:24:00 +0100 [thread overview]
Message-ID: <E1VUm9A-0000cG-AN@mlist.mta.ca> (raw)
Hi,
In a category with a zero object and biproducts we obtain a unique
enrichment in commutative monoids, which we will write as +. If the
category is also monoidal with left and right duals for objects, then
the tensor product distributes over +, in the sense that
f (x) (g+h) = (f (x) g) + (f (x) h)
for all morphisms f,g,h with g and h in the same hom-set.
I have a proof of this but it is a bit clunky, and rather long. Can
anyone give a beautiful one?
Best wishes,
Jamie.
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2013-10-11 12:24 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2013-10-11 12:24 Jamie Vicary [this message]
2013-10-13 7:05 ` Richard Garner
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