From: Tom Leinster <Tom.Leinster@glasgow.ac.uk>
To: <categories@mta.ca>
Subject: What is Isbell completion?
Date: Sun, 6 Mar 2011 22:54:26 +0000 [thread overview]
Message-ID: <E1PweO6-00066u-Iq@mlist.mta.ca> (raw)
Dear All,
Let A be a small category. Isbell conjugacy gives an adjunction between
Set^(A^op) and (Set^A)^op.
Like any adjunction, this restricts in a maximal way to an equivalence
between full subcategories. Write I(A) for either side of that
equivalence.
What is I(A)?
Certainly I(A) contains the Cauchy-completion of A. But it can be
strictly bigger: for example, if A is the initial category then I(A) is
the terminal category. Or, if A is a discrete category with more than one
object then I(A) is A with initial and terminal objects adjoined.
One can also ask the question in an enriched setting.
Best wishes,
Tom
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
reply other threads:[~2011-03-06 22:54 UTC|newest]
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