From: Mamuka Jibladze <jib@rmi.acnet.ge>
To: Categories list <categories@mta.ca>
Subject: Re: Chew on this
Date: Fri, 25 Sep 1998 15:55:51 +0300 (EET DST) [thread overview]
Message-ID: <Pine.GSO.3.96.980925153231.5798C-100000@rmi-sun.rmi.acnet.ge> (raw)
In-Reply-To: <Pine.LNX.3.95.980908134600.10954C-100000@triples.math.mcgill.ca>
One more comment on that fascinating ugly monoidal structure. Many
years ago D. Pataraia as a student was asked to realise tensor product of
vector spaces (V and W over k) as a colimit. He then came up with a
diagram (sorry for still more ugly notation)
k_{v,w}
/ \
/ \
|_ _|
V_w W_v
That is, vertices of the diagram consist of U(W) copies of V, U(V) copies
of W, and U(V)xU(W) copies of k (U is the forgetful functor to sets). And
the maps... well, you guess.
The reason this is relevant is that in the Barr's monoidal category, the
product of (S->U(A)) and (T->U(B)) is (SxT->U(C)) where C is the colimit,
in the category of algebras, of
F(1)_{s,t}
/ \
/ \
|_ _|
A_t B_s
It does not look so ugly after all, does it?
:),
Mamuka
prev parent reply other threads:[~1998-09-25 12:55 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
1998-09-08 17:58 Michael Barr
1998-09-25 12:55 ` Mamuka Jibladze [this message]
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