Category:End-Extensions

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This category contains results about End-Extensions.

Let $\struct {S, \preccurlyeq_S}$ and $\struct {T, \preccurlyeq_T}$ be ordered sets such that $S \subseteq T$.

Let ${\preccurlyeq_S} = {\preccurlyeq_T} {\restriction_S}$ be the restriction of $\preccurlyeq_T$ to $S$.

Let $i_S: S \to T$ denote the inclusion mapping from $S$ to $T$:

$\forall s \in S: \map {i_S} s = s$

Let:

$\forall s \in S: \forall t \in T \setminus S: x \prec_T y$


Then $\struct {T, \preccurlyeq_T}$ is an end-extension of $\struct {S, \preccurlyeq_S}$.

Subcategories

This category has only the following subcategory.