Category:Definitions/Preorder Categories

From ProofWiki
Jump to navigation Jump to search

This category contains definitions related to Preorder Categories.
Related results can be found in Category:Preorder Categories.


Let $\left({S, \precsim}\right)$ be a preordered set.


One can interpret $\left({S, \precsim}\right)$ as being a category, with:

Objects:         The elements of $S$
Morphisms: Precisely one morphism $a \to b$ for every $a, b \in S$ with $a \precsim b$

More formally, we let the morphisms be the elements of the relation ${\precsim} \subseteq S \times S$.

Thus, $a \to b$ in fact denotes the ordered pair $\left({a, b}\right)$.


The category that so arises is called a preorder category.

Pages in category "Definitions/Preorder Categories"

The following 3 pages are in this category, out of 3 total.