[----- The Types Forum, http://www.cis.upenn.edu/~bcpierce/types -----] Is anything known about the following variation on a Galois connection? Given domains X and A with partial orders, f:X->A and g:A->X constitute a *Galois connection* if the following four conditions hold (1) x <= y implies f(x) <= f(y) (2) a <= b implies g(a) <= g(b) (3) x <= g(f(x)) (4) f(g(a)) <= a (This is equivalent to saying f(x) <= a iff x <= g(a).) The same functions constitute a *twisted Galois connection* if we have conditions (1)-(3) and also (4') a <= f(g(a)) Both Galois connections and twisted Galois connections compose. If f:X->A, g:A->X and h:A->Z, k:Z->A consitute a (twisted) Galois connection, then so do f;h:X->Z, k;g:Z->X. Is there anything in the literature about twisted Galois connections or the corresponding notion of a twisted adjoint, perhaps under a different name? Many thanks, -- P ----------------------------------------------------------------------- Philip Wadler wadler@avaya.com www.research.avayalabs.com/user/wadler Avaya Labs, 233 Mount Airy Road, Basking Ridge, NJ 07920 USA phone +1 908 696 5137 fax +1 908 696 5402 ---------------------------------------------------------------------- "When a Mathematical Reasoning can be had it's as great a folly to make use of any other, as to grope for a thing in the dark, when you have a Candle standing by you." John Arbuthnot, 1692 ----------------------------------------------------------------------