From: "Serge P. Kovalyov" <kovalyov@nsc.ru>
To: categories@mta.ca
Subject: Super comma category
Date: Thu, 7 Jan 2010 19:33:39 +0600 (NOVT) [thread overview]
Message-ID: <E1NT4CF-0003VP-M2@mailserv.mta.ca> (raw)
In-Reply-To: <20090218222112.L22481@mx.nsc.ru>
Dear Category Theory gurus,
Is there any literature in which MacLane's "super comma category"
(Cat./.C) of all small diagrams in a category C is studied in details?
Actually I work in its covariant form, where a morphism from a diagram
D:X->C to G:Y->C is a pair (e,F) consisting of a functor F:X->Y and a
natural transformation e:D->GF. For example, is it known that the
embedding of an ordinary comma category Cat/C into Cat./.C preserves
colimits? Also there exists a monad (Cat./.-, d, m) on CAT, where d_C
takes each C-object X to a discrete diagram {X}, and m represents
"drawing" a diagram of diagrams as a diagram. Is its Eilenberg-Moore
category isomorphic to some "familiar" construction?
Thanks,
Serge.
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next parent reply other threads:[~2010-01-07 13:33 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
[not found] <20090218222112.L22481@mx.nsc.ru>
2010-01-07 13:33 ` Serge P. Kovalyov [this message]
2010-01-08 16:13 ` Andree Ehresmann
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