Category:Galois Connections
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This category contains results about Galois Connections.
Definitions specific to this category can be found in Definitions/Galois Connections.
Let $\struct {S, \preceq}$ and $\struct {T, \precsim}$ be ordered sets.
Let $g: S \to T$, $d: T \to S$ be mappings.
Then $\tuple {g, d}$ is a Galois connection if and only if:
- $g$ and $d$ are increasing mappings and
- $\forall s \in S, t \in T: t \precsim \map g s \iff \map d t \preceq s$
Subcategories
This category has only the following subcategory.
Pages in category "Galois Connections"
The following 22 pages are in this category, out of 22 total.
A
G
- Galois Connection Implies Order on Mappings
- Galois Connection implies Upper Adjoint is Surjection iff Lower Adjoint is Injection
- Galois Connection is Expressed by Maximum
- Galois Connection is Expressed by Minimum
- Galois Connection with Upper Adjoint Surjective implies Scond Ordered Set and Image of Lower Adjoint are Isomorphic