Category:Definitions/Compatible Relations
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This category contains definitions related to Compatible Relations.
Related results can be found in Category:Compatible Relations.
Let $\struct {S, \circ}$ be a closed algebraic structure.
Let $\RR$ be a relation on $S$.
Then $\RR$ is compatible with $\circ$ if and only if:
- $\forall x, y, z \in S: x \mathrel \RR y \implies \paren {x \circ z} \mathrel \RR \paren {y \circ z}$
- $\forall x, y, z \in S: x \mathrel \RR y \implies \paren {z \circ x} \mathrel \RR \paren {z \circ y}$
Subcategories
This category has the following 2 subcategories, out of 2 total.
C
O
Pages in category "Definitions/Compatible Relations"
The following 6 pages are in this category, out of 6 total.
R
- Definition:Relation Compatible with Operation
- Definition:Relation Conversely Compatible with Operation
- Definition:Relation Conversely Compatible with Operation/Linguistic Note
- Definition:Relation Strongly Compatible with Operation
- Definition:Relation Strongly Compatible with Operation/Linguistic Note