Category:Definitions/Order Categories
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This category contains definitions related to Order Categories.
Related results can be found in Category:Order Categories.
Let $\struct {S, \preceq}$ be an ordered set.
One can interpret $\struct {S, \preceq}$ as being a category, with:
| Objects: | The elements of $S$ | |
| Morphisms: | Precisely one morphism $a \to b$ for every $a, b \in S$ with $a \preceq b$ |
More formally, we let the morphisms be the elements of the relation ${\preceq} \subseteq S \times S$.
Thus, $a \to b$ in fact denotes the ordered pair $\tuple {a, b}$.
The category that so arises is called an order category.
Pages in category "Definitions/Order Categories"
The following 3 pages are in this category, out of 3 total.