Conditions for adjoints -- another variant

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/ ]