nLab
pseudo-proset
Contents
Context
Category theory
Graph theory
Contents
Idea
Pseudo-preorders are to preorders as pseudo-equivalence relations are to equivalence relations. A set with a pseudo-preorder is then a pseudo-preordered set or a pseudo-proset.
Pseudo-prosets are important because they are the basic structure used to build many other structures like categories and setoids.
Definition
With a family of sets
…
With one set
A pseudo-preorder on a set is a set of morphisms and functions , (a loop directed pseudograph), with functions and
such that
- for every ,
- for every ,
- for every and such that ,
- for every and such that ,
A pseudo-preordered set or pseudo-proset consists of a set with a pseudo-preorder .
Examples
A category is a pseudo-proset which additionally satisfies
-
for every object , , , and and edge , , and
-
for every vertex , and edge
-
for every vertex , and edge
See also
Last revised on September 22, 2022 at 15:16:14.
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