* What is Isbell completion?
@ 2011-03-06 22:54 Tom Leinster
0 siblings, 0 replies; only message in thread
From: Tom Leinster @ 2011-03-06 22:54 UTC (permalink / raw)
To: categories
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/ ]
^ permalink raw reply [flat|nested] only message in thread
only message in thread, other threads:[~2011-03-06 22:54 UTC | newest]
Thread overview: (only message) (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2011-03-06 22:54 What is Isbell completion? Tom Leinster
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).