Re: Conditions for adjoints -- another variant

[Dusko Pavlovic <Dusko.Pavlovic@comlab.ox.ac.uk>]

cca 1991, i mentioned to mike barr that the functoriality of adjoints was
derivable, and he knew it already. i think he said that this was used by
isbell.

(it's embarassing that i remember things from so long ago; and also that i
don't remember them clearly enough to be confident. but does it really
matter? when we optimize, we often find it more efficient not to store
some data, but to regenerate when needed...)

-- dusko

On Sat, 24 Oct 2009, robin@ucalgary.ca wrote:

> 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
>
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>
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>


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