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"twisted" Galois connections?
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
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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
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"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
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