need help with naming

Stream: maths

[Yury G. Kudryashov]

Given a function f : α → β, how would you call g : β → α given by g y = Sup {x | f x ≤ y}? I'm mostly interested in the case of a monotone f but definition works for any f.

[Mario Carneiro]

it looks like a right adjoint to me

[Chris Hughes]

It's a galois connection.