 ##  [Galois Connection](/galois-connection) 

  ##  [Galois Connection](https://natural.quantumdictionary.io/galois-connection-0) 

  
 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)


**Natural &amp; Formal Sciences Dictionary**

 
Definition

A pair of monotone maps between posets (f : P → Q, g : Q → P) such that for all p in P and q in Q, f(p) ≤_Q q iff p ≤_P g(q). Equivalently, f is left adjoint to g when posets are viewed as categories. It yields a residual correspondence tying approximation and closure operators.

 
 ##  [Galois Connection](https://mathlogic.quantumdictionary.io/galois-connection-1) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A pair of monotone maps between partially ordered sets, one left adjoint and one right adjoint, such that one map composed with the other yields order inequalities in both directions (f(a) ≤ b iff a ≤ g(b)); this correspondence links closure-like operations and kernel-like operations and organizes duality between lattices and their images.

 
 ##  [Galois Connection](https://puremath.quantumdictionary.io/galois-connection-2) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

A pair of monotone (order-preserving) maps between posets, L: P→Q and R: Q→P, such that for all p in P and q in Q, L(p) ≤ q if and only if p ≤ R(q); this yields an inclusion-reversing, closure-like correspondence linking the two orders.