From: robin@ucalgary.ca
To: categories@mta.ca
Subject: Conditions for adjoints -- another variant
Date: Sat, 24 Oct 2009 17:11:26 -0600 (MDT) [thread overview]
Message-ID: <E1N1qqu-0002HW-4J@mailserv.mta.ca> (raw)
BTW. Here are some even cleaner conditions ....
There is an adjoint between two categories iff
there are two object functions F and G (not required to be functors) and
For each X \in \X and Y \in \Y there are two functions:
#: \X(X,G(Y)) -> \Y(F(X),Y) ---- sharp
@: \Y(F(X),Y) -> \X(X,G(Y)) ---- flat
(i)' @ and # are inverse @(#(f)) = f and #(@(g)) = g
(ii)' @(h k) = @(h) @(#(1) k) and dually #(xy) = #(x @(1)) #(y)
Still hoping to find where these all are recorded!!
-robin
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2009-10-24 23:11 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2009-10-24 23:11 robin [this message]
2009-10-25 1:03 Dusko Pavlovic
2009-10-25 10:05 Paul Levy
2009-11-01 2:20 Ellis D. Cooper
2009-11-09 23:50 Ellis D. Cooper
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