From: Ross Street <street@ics.mq.edu.au>
To: categories@mta.ca
Subject: Pseudo orbits
Date: Sat, 28 Aug 1999 13:34:35 +1000 [thread overview]
Message-ID: <l03130300b3ed03a7f489@[137.111.7.182]> (raw)
In-Reply-To: <4.2.0.58.19990827154835.00987a70@ichthus.syr.edu>
Dear Gaunce Lewis, GT-colleague and all,
When we regard a monoid M as a one-object category, an M-set is a functor
X : M --> Set and the colimit of the functor X is the set of orbits of
the M-set.
What GT-colleague has is an ordered monoid which can be regarded as a
one-object 2-category M, and the action F of M on the category C
amounts to a 2-functor X : M --> Cat. I suspect that the construction
required is the pseudocolimit of X. This kind of colimit for 2-functors
was considered in the book of John Gray
J.W. Gray, Formal Category Theory: Adjointness for 2-Categories, Lecture
Notes in Math. 391 (Springer, 1974)
and in my paper
Limits indexed by category-valued 2-functors, J. Pure Appl. Algebra 8
(1976) 149-181
where I show that pseudo(co)limits and lax (co)limits are ordinary weighted
(= indexed) (co)limits in the sense of enriched category theory (for the
base monoidal category Cat).
I suspect the condition that the identity element is initial is a red
herring even though this makes it look as though canonical maps are being
inverted rather than isomorphisms being introduced.
Regards,
Ross
prev parent reply other threads:[~1999-08-28 3:34 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
1999-08-27 20:01 looking for references Gaunce Lewis
1999-08-28 3:34 ` Ross Street [this message]
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